POSITIVE SOLUTIONS FOR A DIRICHLET PROBLEM
Institute of Scientific and Technical Information of China (English)
周焕松
2001-01-01
In this paper, we study a nonlinear Dirichlet problem on a smooth bounded domain, in which the nonlinear term is asymptotically linear, not superlinear, at infinity and sublinear near the origin. By using Mountain Pass Theorem, we prove that there exist at least two positive solutions under suitable assumptions on the nonlinearity.
Institute of Scientific and Technical Information of China (English)
WEN Guochun; HUANG Sha; QIAO Yuying
2001-01-01
In 1988, Yu. A. Alkhutov and I. T. Mamedov discussed the solvability of the Dirichlet problem for linear uniformly parabolic equations with measurable coefficients where the coefficients satisfy the condition In this paper, we try to generalize the results of Alkhutov and Mamedov to nonlinear uni-formly parabolic systems of second order equations with measurable coefficients; moreover,we also discuss the solvability of the Neumann problem for the above systems.
Dirichlet Problem on the Upper Half Space
Indian Academy of Sciences (India)
Dewu Yang; Yudong Ren
2014-05-01
In this paper, a solution of the Dirichlet problem on the upper half space for a fast growing continuous boundary function is constructed by the generalized Dirichlet integral with this boundary function.
Directory of Open Access Journals (Sweden)
Tomasz S. Zabawa
2005-01-01
Full Text Available The Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations of elliptic type is considered. It is shown the existence of solutions to this problem. The result is based on Chaplygin's method of lower and upper functions.
On Existence and Stability of Solutions for Higher Order Semilinear Dirichlet Problems
Indian Academy of Sciences (India)
Marek Galewski
2008-11-01
We provide existence and stability results for semilinear Dirichlet problems with nonlinearity satisfying general growth conditions. We consider the case when both the coefficients of the differential operator and the nonlinear term depend on the numerical parameter. We show applications for the fourth order semilinear Dirichlet problem.
The Dirichlet problem for the minimal surface equation
Williams, Graham H.
1996-01-01
The minimal surface equation is an elliptic equation but it is nonlinear and is not uniformly elliptic. It is the Euler-Lagrange equation for variational problems which involve minimising the area of the graphs of functions. For the most part we will solve the variational problem with Dirichlet boundary values, that is, when the values of the function are prescribed on the boundary of some given set. We will present some existence results using the Direct Method from the Calcul...
Institute of Scientific and Technical Information of China (English)
谢腊兵; 江福汝
2003-01-01
The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations. The asymptotic expansions of solution were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application of the method of boundary layer with multiple scales.
A Note on Existence and Stability of Solutions for Semilinear Dirichlet Problems
Indian Academy of Sciences (India)
Marek Galewski
2011-05-01
We provide existence and stability results for a fourth-order semilinear Dirichlet problem in the case when both the coefficients of the differential operator and the nonlinear term depend on the numerical parameter. We use a dual variational method.
On the coupled NBEM and FEM for a class of nonlinear exterior Dirichlet problem in R2
Institute of Scientific and Technical Information of China (English)
WU; Zhengpeng; KANG; Tong; YU; Dehao
2004-01-01
In this paper, based on the natural boundary reduction advanced by Feng and Yu, we couple the finite elementapproach with the natural boundary element method to study theweak solvability and Galerkin approximation of a class ofnonlinear exterior boundary value problems. The analysis is mainlybased on the variational formulation with constraints.We provethe error estimate of the finite element solution and obtain theasymptotic rate of convergence. Finally, we also give anumerical example.
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Imed Bachar
2014-01-01
Full Text Available We are interested in the following fractional boundary value problem: Dαu(t+atuσ=0, t∈(0,∞, limt→0t2-αu(t=0, limt→∞t1-αu(t=0, where 1<α<2, σ∈(-1,1, Dα is the standard Riemann-Liouville fractional derivative, and a is a nonnegative continuous function on (0,∞ satisfying some appropriate assumptions related to Karamata regular variation theory. Using the Schauder fixed point theorem, we prove the existence and the uniqueness of a positive solution. We also give a global behavior of such solution.
Uniqueness Result in the Cauchy Dirichlet Problem via Mehler Kernel
Dhungana, Bishnu P.
2014-09-01
Using the Mehler kernel, a uniqueness theorem in the Cauchy Dirichlet problem for the Hermite heat equation with homogeneous Dirichlet boundary conditions on a class P of bounded functions U( x, t) with certain growth on U x ( x, t) is established.
Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian
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Dorota Bors
2014-01-01
Dirichlet boundary data. Some sufficient condition under which the solutions of the equations considered depend continuously on parameters is stated. The application of the results to some optimal control problem is presented. The methods applied in the paper make use of the variational structure of the problem.
Stability of nonlinear Dirichlet BVPs governed by fractional Laplacian.
Bors, Dorota
2014-01-01
We consider a class of partial differential equations with the fractional Laplacian and the homogeneous Dirichlet boundary data. Some sufficient condition under which the solutions of the equations considered depend continuously on parameters is stated. The application of the results to some optimal control problem is presented. The methods applied in the paper make use of the variational structure of the problem.
Dirichlet problem for a second order singular differential equation
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Wenshu Zhou
2006-12-01
Full Text Available This article concerns the existence of positive solutions to the Dirichlet problem for a second order singular differential equation. To prove existence, we use the classical method of elliptic regularization.
On the Uniqueness Result for the Dirichlet Problem and Invexity
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M. Płócienniczak
2008-08-01
Full Text Available We provide an existence and uniqueness theorem for the Dirichlet problem div Hz(y,Ñx(y=ÑxF(y,x(y.The assumption that both H and F are invex with respect to the second variable is imposed and the direct variational method is applied. The applicationis also shown.
Dirichlet Problem for Hermitian-Einstein Equation over Almost Hermitian Manifold
Institute of Scientific and Technical Information of China (English)
Yue WANG; Xi ZHANG
2012-01-01
In this paper,we investigate the Dirichlet problem for Hermitian-Einstein equation on complex vector bundle over almost Hermitian manifold,and we obtain the unique solution of the Dirichlet problem for Hermitian-Einstein equation.
Imitation learning of Non-Linear Point-to-Point Robot Motions using Dirichlet Processes
DEFF Research Database (Denmark)
Krüger, Volker; Tikhanoff, Vadim; Natale, Lorenzo
2012-01-01
In this paper we discuss the use of the infinite Gaussian mixture model and Dirichlet processes for learning robot movements from demonstrations. Starting point of this work is an earlier paper where the authors learn a non-linear dynamic robot movement model from a small number of observations....... The model in that work is learned using a classical finite Gaussian mixture model (FGMM) where the Gaussian mixtures are appropriately constrained. The problem with this approach is that one needs to make a good guess for how many mixtures the FGMM should use. In this work, we generalize this approach...
On an asymptotically linear elliptic Dirichlet problem
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Zhitao Zhang
2002-01-01
Full Text Available Under very simple conditions, we prove the existence of one positive and one negative solution of an asymptotically linear elliptic boundary value problem. Even for the resonant case at infinity, we do not need to assume any more conditions to ensure the boundness of the (PS sequence of the corresponding functional. Moreover, the proof is very simple.
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Ishfaq Ahmad Ganaie
2014-01-01
Full Text Available Cubic Hermite collocation method is proposed to solve two point linear and nonlinear boundary value problems subject to Dirichlet, Neumann, and Robin conditions. Using several examples, it is shown that the scheme achieves the order of convergence as four, which is superior to various well known methods like finite difference method, finite volume method, orthogonal collocation method, and polynomial and nonpolynomial splines and B-spline method. Numerical results for both linear and nonlinear cases are presented to demonstrate the effectiveness of the scheme.
A sign-changing solution for a superlinear Dirichlet problem, II
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Alfonso Castro
2003-02-01
Full Text Available In previous work by Castro, Cossio, and Neuberger cite{ccn}, it was shown that a superlinear Dirichlet problem has at least three nontrivial solutions when the derivative of the nonlinearity at zero is less than the first eigenvalue of $-Delta$ with zero Dirichlet boundry condition. One of these solutions changes sign exactly-once and the other two are of one sign. In this paper we show that when this derivative is between the $k$-th and $k+1$-st eigenvalues there still exists a solution which changes sign at most $k$ times. In particular, when $k=1$ the sign-changing {it exactly-once} solution persists although one-sign solutions no longer exist.
Macías-Díaz, J E; 10.1002/zamm.200700172
2011-01-01
In this work, we present a conditionally stable finite-difference scheme that consistently approximates the solution of a general class of (3+1)-dimensional nonlinear equations that generalizes in various ways the quantitative model governing discrete arrays consisting of coupled harmonic oscillators. Associated with this method, there exists a discrete scheme of energy that consistently approximates its continuous counterpart. The method has the properties that the associated rate of change of the discrete energy consistently approximates its continuous counterpart, and it approximates both a fully continuous medium and a spatially discretized system. Conditional stability of the numerical technique is established, and applications are provided to the existence of the process of nonlinear supratransmission in generalized Klein-Gordon systems and the propagation of binary signals in semi-unbounded, three-dimensional arrays of harmonic oscillators coupled through springs and perturbed harmonically at the bound...
Regularity of spectral fractional Dirichlet and Neumann problems
DEFF Research Database (Denmark)
Grubb, Gerd
2016-01-01
Consider the fractional powers and of the Dirichlet and Neumann realizations of a second-order strongly elliptic differential operator A on a smooth bounded subset Ω of . Recalling the results on complex powers and complex interpolation of domains of elliptic boundary value problems by Seeley...... in the 1970's, we demonstrate how they imply regularity properties in full scales of -Sobolev spaces and Hölder spaces, for the solutions of the associated equations. Extensions to nonsmooth situations for low values of s are derived by use of recent results on -calculus. We also include an overview...
A note on the Dirichlet problem for model complex partial differential equations
Ashyralyev, Allaberen; Karaca, Bahriye
2016-08-01
Complex model partial differential equations of arbitrary order are considered. The uniqueness of the Dirichlet problem is studied. It is proved that the Dirichlet problem for higher order of complex partial differential equations with one complex variable has infinitely many solutions.
Dirichlet-to-Neumann boundary conditions for multiple scattering problems
Grote, Marcus J.; Kirsch, Christoph
2004-12-01
A Dirichlet-to-Neumann (DtN) condition is derived for the numerical solution of time-harmonic multiple scattering problems, where the scatterer consists of several disjoint components. It is obtained by combining contributions from multiple purely outgoing wave fields. The DtN condition yields an exact non-reflecting boundary condition for the situation, where the computational domain and its exterior artificial boundary consist of several disjoint components. Because each sub-scatterer can be enclosed by a separate artificial boundary, the computational effort is greatly reduced and becomes independent of the relative distances between the different sub-domains. The DtN condition naturally fits into a variational formulation of the boundary-value problem for use with the finite element method. Moreover, it immediately yields as a by-product an exact formula for the far-field pattern of the scattered field. Numerical examples show that the DtN condition for multiple scattering is as accurate as the well-known DtN condition for single scattering problems [J. Comput. Phys. 82 (1989) 172; Numerical Methods for Problems in Infinite Domains, Elsevier, Amsterdam, 1992], while being more efficient due to the reduced size of the computational domain.
On some nonlinear potential problems
Directory of Open Access Journals (Sweden)
M. A. Efendiev
1999-05-01
Full Text Available The degree theory of mappings is applied to a two-dimensional semilinear elliptic problem with the Laplacian as principal part subject to a nonlinear boundary condition of Robin type. Under some growth conditions we obtain existence. The analysis is based on an equivalent coupled system of domain--boundary variational equations whose principal parts are the Dirichlet bilinear form in the domain and the single layer potential bilinear form on the boundary, respectively. This system consists of a monotone and a compact part. Additional monotonicity implies convergence of an appropriate Richardson iteration.
On the Dirichlet Problem of Mixed Type for Lower Hybrid Waves in Axisymmetric Cold Plasmas
Lupo, Daniela; Monticelli, Dario D.; Payne, Kevin R.
2015-07-01
For a class of linear second order partial differential equations of mixed elliptic-hyperbolic type, which includes a well known model for analyzing possible heating in axisymmetric cold plasmas, we give results on the weak well-posedness of the Dirichlet problem and show that such solutions are characterized by a variational principle. The weak solutions are shown to be saddle points of natural functionals suggested by the divergence form of the PDEs. Moreover, the natural domains of the functionals are the weighted Sobolev spaces to which the solutions belong. In addition, all critical levels will be characterized in terms of global extrema of the functionals restricted to suitable infinite dimensional linear subspaces. These subspaces are defined in terms of a robust spectral theory with weights which is associated to the linear operator and is developed herein. Similar characterizations for the weighted eigenvalue problem and nonlinear variants will also be given. Finally, topological methods are employed to obtain existence results for nonlinear problems including perturbations in the gradient which are then applied to the well-posedness of the linear problem with lower order terms.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The authors consider the existence of singular limit solutions for a family of nonlinear elliptic problems with exponentially dominated nonlinearity and Dirichlet boundary condition and generalize the results of [3].
CFT dual of the AdS Dirichlet problem : Fluid/Gravity on cut-off surfaces
Brattan, Daniel K; Loganayagam, R; Rangamani, Mukund
2011-01-01
We study the gravitational Dirichlet problem in AdS spacetimes with a view to understanding the boundary CFT interpretation. We define the problem as bulk Einstein's equations with Dirichlet boundary conditions on fixed timelike cut-off hypersurface. Using the fluid/gravity correspondence, we argue that one can determine non-linear solutions to this problem in the long wavelength regime. On the boundary we find a conformal fluid with Dirichlet constitutive relations, viz., the fluid propagates on a `dynamical' background metric which depends on the local fluid velocities and temperature. This boundary fluid can be re-expressed as an emergent hypersurface fluid which is non-conformal but has the same value of the shear viscosity as the boundary fluid. The hypersurface dynamics arises as a collective effect, wherein effects of the background are transmuted into the fluid degrees of freedom. Furthermore, we demonstrate that this collective fluid is forced to be non-relativistic below a critical cut-off radius in...
Institute of Scientific and Technical Information of China (English)
YIN WeiPing; YIN XiaoLan
2009-01-01
Complex Monge-Amlère equation is a nonlinear equation with high degree,so its solutio nis very difficult to get. How to get the plurisubharmonic solution of Dirichlet problem of complex MongeAmpere equation on the Cartan-Hartogs domain of the second type is discussed by using the analytic order ordinary differential equation (ODE) by using quite different method. Secondly,the solution of the Dirichlet problem is given in semi-explicit formula,and under a special case the exact solution is obtained. These results may be helpful for the numerical method of Dirichlet problem of complex Monge-Ampere equation on the Cartan-Hartogs domain.
Dirichlet-Neumann bracketing for boundary-value problems on graphs
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Sonja Currie
2005-08-01
Full Text Available We consider the spectral structure of second order boundary-value problems on graphs. A variational formulation for boundary-value problems on graphs is given. As a consequence we can formulate an analogue of Dirichlet-Neumann bracketing for boundary-value problems on graphs. This in turn gives rise to eigenvalue and eigenfunction asymptotic approximations.
An analytic mapping property of the Dirichlet-to-Neumann operator in Helmholtz boundary problems
DEFF Research Database (Denmark)
Karamehmedovic, Mirza
The analytic version of microlocal analysis shows that if the boundary and the Dirichlet datum of a Helmholtz boundary value problem are real-analytic, then so is the corresponding Neumann datum. However, the domain of ana-lytic continuation of the Neumann datum is, in general, unknown. We shall...... here relate, in terms of explicit estimates, the domains of analytic continua-tion of Dirichlet and Neumann boundary data for Helmholtz problems in two or more independent variables, and in neighbourhoods of planar pieces of the boundary. For this purpose, we shall characterise a special subspace...
A Viscosity Approach to the Dirichlet Problem for Complex Monge-Amp\\`ere Equations
Wang, Yu
2010-01-01
The Dirichlet problem for complex Monge-Amp\\'ere equations with continuous data is considered. In particular, a notion of viscosity solutions is introduced; a comparison principle and a solvability theorem are proved; the equivalence between viscosity and pluripotential solutions is established; and an ABP-type of $L^{\\infty}$-estimate is achieved.
The Graviton in the AdS-CFT correspondence Solution via the Dirichlet Boundary value problem
Mück, W
1998-01-01
Using the AdS-CFT correspondence we calculate the two point function of CFT energy momentum tensors. The AdS gravitons are considered by explicitly solving the Dirichlet boundary value problem for $x_0=\\epsilon$. We consider this treatment as complementary to existing work, with which we make contact.
Lee, Kuo-Wei
2016-01-01
We prove the existence and uniqueness of the Dirichlet problem for spacelike, spherically symmetric, constant mean curvature equation with symmetric boundary data in the extended Schwarzschild spacetime. As an application, we completely solve the CMC foliation conjecture which is posted by Malec and O Murchadha in 2003.
Lee, Kuo-Wei
2016-09-01
We prove the existence and uniqueness of the Dirichlet problem for the spacelike, spherically symmetric, constant mean curvature equation with symmetric boundary data in the extended Schwarzschild spacetime. As an application, we completely solve the CMC foliation conjecture which is proposed by Malec and Murchadha (2003 Phys. Rev. D 68 124019).
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Maria Transirico
2008-10-01
Full Text Available This paper is concerned with the study of the Dirichlet problem for a class of second-order linear elliptic equations in weighted Sobolev spaces on unbounded domains of Ã¢Â„Ân, nÃ¢Â‰Â¥3. We state a regularity result and we can deduce an existence and uniqueness theorem.
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Boccia Serena
2008-01-01
Full Text Available This paper is concerned with the study of the Dirichlet problem for a class of second-order linear elliptic equations in weighted Sobolev spaces on unbounded domains of , . We state a regularity result and we can deduce an existence and uniqueness theorem.
T, M P Ramirez
2012-01-01
Using a conjecture that allows to approach separable-variables conductivity functions, the elements of the Modern Pseudoanalytic Function Theory are used, for the first time, to numerically solve the Dirichlet boundary value problem of the two-dimensional Electrical Impedance Equation, when the conductivity function arises from geometrical figures, located within bounded domains.
Solution of the Dirichlet Problem for the Poisson's Equation in a Multidimensional Infinite Layer
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O. D. Algazin
2015-01-01
Full Text Available The paper considers the multidimensional Poisson equation in the domain bounded by two parallel hyperplanes (in the multidimensional infinite layer. For an n-dimensional half-space method of solving boundary value problems for linear partial differential equations with constant coefficients is a Fourier transform to the variables in the boundary hyperplane. The same method can be used for an infinite layer, as is done in this paper in the case of the Dirichlet problem for the Poisson equation. For strip and infinite layer in three-dimensional space the solutions of this problem are known. And in the three-dimensional case Green's function is written as an infinite series. In this paper, the solution is obtained in the integral form and kernels of integrals are expressed in a finite form in terms of elementary functions and Bessel functions. A recurrence relation between the kernels of integrals for n-dimensional and (n + 2 -dimensional layers was obtained. In particular, is built the Green's function of the Laplace operator for the Dirichlet problem, through which the solution of the problem is recorded. Even in three-dimensional case we obtained new formula compared to the known. It is shown that the kernel of the integral representation of the solution of the Dirichlet problem for a homogeneous Poisson equation (Laplace equation is an approximate identity (δ-shaped system of functions. Therefore, if the boundary values are generalized functions of slow growth, the solution of the Dirichlet problem for the homogeneous equation (Laplace is written as a convolution of kernels with these functions.
The Dirichlet problem with L2-boundary data for elliptic linear equations
Chabrowski, Jan
1991-01-01
The Dirichlet problem has a very long history in mathematics and its importance in partial differential equations, harmonic analysis, potential theory and the applied sciences is well-known. In the last decade the Dirichlet problem with L2-boundary data has attracted the attention of several mathematicians. The significant features of this recent research are the use of weighted Sobolev spaces, existence results for elliptic equations under very weak regularity assumptions on coefficients, energy estimates involving L2-norm of a boundary data and the construction of a space larger than the usual Sobolev space W1,2 such that every L2-function on the boundary of a given set is the trace of a suitable element of this space. The book gives a concise account of main aspects of these recent developments and is intended for researchers and graduate students. Some basic knowledge of Sobolev spaces and measure theory is required.
MODIFIED LEAST SQUARE METHOD ON COMPUTING DIRICHLET PROBLEMS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The singularity theory of dynamical systems is linked to the numerical computation of boundary value problems of differential equations. It turns out to be a modified least square method for a calculation of variational problem defined on Ck(Ω), in which the base functions are polynomials and the computation of problems is transferred to compute the coefficients of the base functions. The theoretical treatment and some simple examples are provided for understanding the modification procedure of the metho...
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Bashir Ahmad
2010-01-01
Full Text Available We study a Dirichlet boundary value problem for Langevin equation involving two fractional orders. Langevin equation has been widely used to describe the evolution of physical phenomena in fluctuating environments. However, ordinary Langevin equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractal medium, numerous generalizations of Langevin equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Langevin equation. This gives rise to the fractional Langevin equation with a single index. Recently, a new type of Langevin equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space.
Institute of Scientific and Technical Information of China (English)
Wang Zhigang; Li Yachun
2012-01-01
The aim of this paper is to prove the well-posedness (existence and uniqueness)of the Lp entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with Lp initial value.We use the device of doubling variables and some technical analysis to prove the uniqueness result.Moreover we can prove that the Lp entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.
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Marco Biroli
2007-12-01
Full Text Available We consider a measure valued map α(u deﬁned on D where D is a subspace of L^p(X,m with X a locally compact Hausdorff topological space with a distance under which it is a space of homogeneous type. Under assumptions of convexity, Gateaux differentiability and other assumptions on α which generalize the properties of the energy measure of a Dirichlet form, we prove the Holder continuity of the local solution u of the problem ∫Xµ(u,v(dx = 0 for each v belonging to a suitable space of test functions, where µ(u,v =< α'(u,v >.
A Note on a Singular Dirichlet Problem%关于一个奇异Dirichlet问题的注记
Institute of Scientific and Technical Information of China (English)
王俊禹; 高文杰
2005-01-01
The Dirichlet problem to a second order differential equation with some singularities is studied. Some existence results are established to the problem which generalize some results recently obtained by D. O'Regan by eliminating some superfluous constrains to the problem. Also, some new results have been proven which may provide more useful information for the study of the problem.
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M. G. Crandall
1999-07-01
Full Text Available We study existence of continuous weak (viscosity solutions of Dirichlet and Cauchy-Dirichlet problems for fully nonlinear uniformly elliptic and parabolic equations. Two types of results are obtained in contexts where uniqueness of solutions fails or is unknown. For equations with merely measurable coefficients we prove solvability of the problem, while in the continuous case we construct maximal and minimal solutions. Necessary barriers on external cones are also constructed.
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Т. Horsin
2014-01-01
Full Text Available We consider an optimal control problem associated to Dirichlet boundary valueproblem for linear elliptic equations on a bounded domain Ω. We take the matrixvalued coecients A(x of such system as a control in L1(Ω;RN RN. One of the important features of the admissible controls is the fact that the coecient matrices A(x are non-symmetric, unbounded on Ω, and eigenvalues of the symmetric part Asym = (A + At=2 may vanish in Ω.
Sobolev spaces of maps and the Dirichlet problem for harmonic maps
Pigola, Stefano; Veronelli, Giona
2014-01-01
In this paper we prove the existence of a solution to the Dirichlet problem for harmonic maps into a geodesic ball on which the squared distance function from the origin is strictly convex. This improves a celebrated theorem obtained by S. Hildebrandt, H. Kaul and K. Widman in 1977. In particular no curvature assumptions on the target are required. Our proof relies on a careful analysis of the Sobolev spaces of maps involved in the variational process, and on a deformation result which permit...
Nonlinear Second-Order Multivalued Boundary Value Problems
Indian Academy of Sciences (India)
Leszek Gasiński; Nikolaos S Papageorgiou
2003-08-01
In this paper we study nonlinear second-order differential inclusions involving the ordinary vector -Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems, namely the Dirichlet, the Neumann and the periodic problems. Using notions and techniques from the nonlinear operatory theory and from multivalued analysis, we obtain solutions for both the `convex' and `nonconvex' problems. Finally, we present the cases of special interest, which fit into our framework, illustrating the generality of our results.
An Inverse Eigenvalue Problem for a Vibrating String with Two Dirichlet Spectra
Rundell, William
2013-04-23
A classical inverse problem is "can you hear the density of a string clamped at both ends?" The mathematical model gives rise to an inverse Sturm-Liouville problem for the unknown density ñ, and it is well known that the answer is negative: the Dirichlet spectrum from the clamped end-point conditions is insufficient. There are many known ways to add additional information to gain a positive answer, and these include changing one of the boundary conditions and recomputing the spectrum or giving the energy in each eigenmode-the so-called norming constants. We make the assumption that neither of these changes are possible. Instead we will add known mass-densities to the string in a way we can prescribe and remeasure the Dirichlet spectrum. We will not be able to answer the uniqueness question in its most general form, but will give some insight to what "added masses" should be chosen and how this can lead to a reconstruction of the original string density. © 2013 Society for Industrial and Applied Mathematics.
INFINITELY MANY SOLUTIONS OF DIRICHLET PROBLEM FOR p－MEAN CURVATURE OPERATOR
Institute of Scientific and Technical Information of China (English)
ChenZhihui; ShenYaotian
2003-01-01
The existence of infinitely many solutions of the following Dirichlet problem for p-mean curvature operator:{-div((1+|△↓u|2)p-2/2△↓u)=f(x,u),x∈Ω. u∈W1-p 0(Ω）. is considered,where Ωis a bounded domain in Rn(n>P>1)with smooth boundary δΩ.Under some natural conditions together with some conditions weaker than(AR)condition,we prove that the above problem has infinitely many solutions by a symmetric version of the Mountain Pass Theorem if f(x,u)/|u|p-2 u→+∞asu→∞.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Dirichlet boundary value problems for perturbed second-order differential equations on a half line are investigated in this paper. The methods mainly depend on the calculus of variations to the classical functionals. Sufficient conditions are obtained for the existence of the solutions.
Marco Pedro Ramirez-Tachiquin; Cesar Marco Antonio Robles Gonzalez; Rogelio Adrian Hernandez-Becerril; Ariana Guadalupe Bucio Ramirez
2013-01-01
Based upon the elements of the modern pseudoanalytic function theory, we analyze a new method for numerically solving the forward Dirichlet boundary value problem corresponding to the two-dimensional electrical impedance equation. The analysis is performed by introducing interpolating piecewise separable-variables conductivity functions in the unit circle. To warrant the effectiveness of the posed method, we consider several examples of conductivity functions, whose boundary condi...
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Le Thi Phuong Ngoc
2016-01-01
Full Text Available This paper is devoted to the study of a nonlinear Carrier wave equation in an annular membrane associated with Robin-Dirichlet conditions. Existence and uniqueness of a weak solution are proved by using the linearization method for nonlinear terms combined with the Faedo-Galerkin method and the weak compact method. Furthermore, an asymptotic expansion of a weak solution of high order in a small parameter is established.
März, Thomas
2010-01-01
Here we study the Dirichlet problem for first order linear and quasi-linear hyperbolic PDEs on a simply connected bounded domain of $\\R^2$, where the domain has an interior outflow set and a mere inflow boundary. By means of a Lyapunov function we show the existence of a unique solution in the space of functions of bounded variation and its continuous dependence on all the data of the linear problem. Finally, we conclude the existence of a solution to the quasi-linear case by utilizing the Schauder fixed point theorem. This type of problems considered here appears in applications such as transport based image inpainting.
On the solvability of Dirichlet problem for the weighted p-Laplacian
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Ewa Szlachtowska
2012-01-01
Full Text Available The paper investigates the existence and uniqueness of weak solutions for a non-linear boundary value problem involving the weighted \\(p\\-Laplacian. Our approach is based on variational principles and representation properties of the associated spaces.
Yan, Yan
2015-01-01
We study a new optimization scheme that generates smooth and robust solutions for Dirichlet velocity boundary control (DVBC) of conjugate heat transfer (CHT) processes. The solutions to the DVBC of the incompressible Navier-Stokes equations are typically nonsmooth, due to the regularity degradation of the boundary stress in the adjoint Navier-Stokes equations. This nonsmoothness is inherited by the solutions to the DVBC of CHT processes, since the CHT process couples the Navier-Stokes equations of fluid motion with the convection-diffusion equations of fluid-solid thermal interaction. Our objective in the CHT boundary control problem is to select optimally the fluid inflow profile that minimizes an objective function that involves the sum of the mismatch between the temperature distribution in the fluid system and a prescribed temperature profile and the cost of the control.Our strategy to resolve the nonsmoothness of the boundary control solution is based on two features, namely, the objective function with a regularization term on the gradient of the control profile on both the continuous and the discrete levels, and the optimization scheme with either explicit or implicit smoothing effects, such as the smoothed Steepest Descent and the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) methods. Our strategy to achieve the robustness of the solution process is based on combining the smoothed optimization scheme with the numerical continuation technique on the regularization parameters in the objective function. In the section of numerical studies, we present two suites of experiments. In the first one, we demonstrate the feasibility and effectiveness of our numerical schemes in recovering the boundary control profile of the standard case of a Poiseuille flow. In the second one, we illustrate the robustness of our optimization schemes via solving more challenging DVBC problems for both the channel flow and the flow past a square cylinder, which use initial
Existence of Positive Solutions to Semipositone Singular Dirichlet Boundary Value Problems
Institute of Scientific and Technical Information of China (English)
Svatoslav STAN(E)K
2006-01-01
The paper presents the conditions which guarantee that for some positive value of μ there are positive solutions of the differential equation (φ(x'))' +μQ(t, x, x') = 0 satisfying the Dirichlet boundary conditions x(0) = x(T) = 0. Here Q is a continuous function on the set [0, T] × (0, ∞) × (R \\ {0}) of the semipositone type and Q is singular at the value zero of its phase variables.
Caplan, R M
2011-01-01
An easy to implement modulus-squared Dirichlet (MSD) boundary condition is formulated for numerical simulations of time-dependent complex partial differential equations in multidimensional settings. The MSD boundary condition approximates a constant modulus-square value of the solution at the boundaries. Application of the MSD boundary condition to the nonlinear Schr\\"odinger equation is shown, and numerical simulations are performed to demonstrate its usefulness and advantages over other simple boundary conditions.
Directory of Open Access Journals (Sweden)
Zhiren Jin
2008-02-01
Full Text Available We prove growth rate estimates and existence of solutions to Dirichlet problems for prescribed mean curvature equation on unbounded domains inside the complement of a cone or a parabola like region in $mathbb{R}^n$ ($ngeq 2$. The existence results are proved using a modified Perron's method by which a subsolution is a solution to the minimal surface equation, while the role played by a supersolution is replaced by estimates on the uniform $C^{0}$ bounds on the liftings of subfunctions on compact sets.
Problems in nonlinear resistive MHD
Energy Technology Data Exchange (ETDEWEB)
Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L. [General Atomics, San Diego, CA (United States)
1998-12-31
Two experimentally relevant problems can relatively easily be tackled by nonlinear MHD codes. Both problems require plasma rotation in addition to the nonlinear mode coupling and full geometry already incorporated into the codes, but no additional physics seems to be crucial. These problems discussed here are: (1) nonlinear coupling and interaction of multiple MHD modes near the B limit and (2) nonlinear coupling of the m/n = 1/1 sawtooth mode with higher n gongs and development of seed islands outside q = 1.
Reimer, Ashton S.; Cheviakov, Alexei F.
2013-03-01
A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.
Antonopoulou, D. C.; Kamvissis, S.
2016-10-01
We present a short note on the extension of the results of Antonopoulou and Kamvissis 2015 Nonlinearity 28 3073-99 to the case of non-zero initial data. More specifically, the defocusing cubic NLS equation is considered on the half-line with decaying (in time) Dirichlet data and sufficiently smooth and decaying (in space) initial data. We prove that for this case also, and for a large class of decaying Dirichlet data, the Neumann data are sufficiently decaying so that the Fokas unified method for the solution of defocusing NLS is applicable.
T., M P Ramirez; Hernandez-Becerril, R A
2012-01-01
Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation. The analysis is performed by interpolating piecewise separable-variables conductivity functions, that are eventually used in the numerical calculations in order to obtain finite sets of orthonormal functions, whose linear combinations succeed to approach the imposed boundary conditions. To warrant the effectiveness of the numerical method, we study six different examples of conductivity. The boundary condition for every case is selected considering one exact solution of the Electrical Impedance Equation. The work intends to discuss the contributions of these results into the field of the Electrical Impedance Tomography.
Kashirin, A. A.; Smagin, S. I.; Taltykina, M. Yu.
2016-04-01
Interior and exterior three-dimensional Dirichlet problems for the Helmholtz equation are solved numerically. They are formulated as equivalent boundary Fredholm integral equations of the first kind and are approximated by systems of linear algebraic equations, which are then solved numerically by applying an iteration method. The mosaic-skeleton method is used to speed up the solution procedure.
Khapaev, M. M.; Khapaeva, T. M.
2016-10-01
A functional-based variational method is proposed for finding the eigenfunctions and eigenvalues in the Sturm-Liouville problem with Dirichlet boundary conditions at the left endpoint and Neumann conditions at the right endpoint. Computations are performed for three potentials: sin(( x-π)2/π), cos(4 x), and a high nonisosceles triangle.
Directory of Open Access Journals (Sweden)
Nguyen Anh Dao
2016-11-01
Full Text Available We prove the existence and uniqueness of singular solutions (fundamental solution, very singular solution, and large solution of quasilinear parabolic equations with absorption for Dirichlet boundary condition. We also show the short time behavior of singular solutions as t tends to 0.
Directory of Open Access Journals (Sweden)
P. A. Krutitskii
2012-01-01
Full Text Available We study the Dirichlet problem for the 2D Laplace equation in a domain bounded by smooth closed curves and smooth cracks. In the formulation of the problem, we do not require compatibility conditions for Dirichlet's boundary data at the tips of the cracks. However, if boundary data satisfies the compatibility conditions at the tips of the cracks, then this is a particular case of our problem. The cases of both interior and exterior domains are considered. The well-posed formulation of the problem is given, theorems on existence and uniqueness of a classical solution are proved, and the integral representation for a solution is obtained. It is shown that weak solution of the problem does not typically exist, though the classical solution exists. The asymptotic formulae for singularities of a solution gradient at the tips of the cracks are presented.
On a nonlinear elliptic problem with critical potential in R2
Institute of Scientific and Technical Information of China (English)
SHEN; Yaotian; YAO; Yangxin; HEN; Zhihui
2004-01-01
Consider the existence of nontrivial solutions of homogeneous Dirichlet problem for a nonlinear elliptic equation with the critical potential in R2. By establishing a weighted inequality with the best constant, determine the critical potential in R2, and study the eigenvalues of Laplace equation with the critical potential. By the Pohozaev identity of a solution with a singular point and the Cauchy-Kovalevskaya theorem, obtain the nonexistence result of solutions with singular points to the nonlinear elliptic equation. Moreover, for the same problem, the existence results of multiple solutions are proved by the mountain pass theorem.
Crasta, Graziano; Fragalà, Ilaria
2015-12-01
Given an open bounded subset Ω of {{R}^n}, which is convex and satisfies an interior sphere condition, we consider the pde {-Δ_{∞} u = 1} in Ω, subject to the homogeneous boundary condition u = 0 on ∂Ω. We prove that the unique solution to this Dirichlet problem is power-concave (precisely, 3/4 concave) and it is of class C 1( Ω). We then investigate the overdetermined Serrin-type problem, formerly considered in Buttazzo and Kawohl (Int Math Res Not, pp 237-247, 2011), obtained by adding the extra boundary condition {|nabla u| = a} on ∂Ω; by using a suitable P-function we prove that, if Ω satisfies the same assumptions as above and in addition contains a ball which touches ∂Ω at two diametral points, then the existence of a solution to this Serrin-type problem implies that necessarily the cut locus and the high ridge of Ω coincide. In turn, in dimension n = 2, this entails that Ω must be a stadium-like domain, and in particular it must be a ball in case its boundary is of class C 2.
Energy Technology Data Exchange (ETDEWEB)
Jamet, P. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1967-07-01
This report gives a general presentation of barrier theory for finite difference operators, with its applications to some boundary value problems. (author) [French] Ce rapport est un expose synthetique de la theorie des barrieres pour les operateurs aux differences finies et ses applications a certaines classes de problemes lineaires elliptiques du 'type de Dirichlet'. (auteur)
A NONLINEAR FEASIBILITY PROBLEM HEURISTIC
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Sergio Drumond Ventura
2015-04-01
Full Text Available In this work we consider a region S ⊂ given by a finite number of nonlinear smooth convex inequalities and having nonempty interior. We assume a point x 0 is given, which is close in certain norm to the analytic center of S, and that a new nonlinear smooth convex inequality is added to those defining S (perturbed region. It is constructively shown how to obtain a shift of the right-hand side of this inequality such that the point x 0 is still close (in the same norm to the analytic center of this shifted region. Starting from this point and using the theoretical results shown, we develop a heuristic that allows us to obtain the approximate analytic center of the perturbed region. Then, we present a procedure to solve the problem of nonlinear feasibility. The procedure was implemented and we performed some numerical tests for the quadratic (random case.
New directions in Dirichlet forms
Jost, Jürgen; Mosco, Umberto; Rockner, Michael; Sturm, Karl-Theodor
1998-01-01
The theory of Dirichlet forms brings together methods and insights from the calculus of variations, stochastic analysis, partial differential and difference equations, potential theory, Riemannian geometry and more. This book features contributions by leading experts and provides up-to-date, authoritative accounts on exciting developments in the field and on new research perspectives. Topics covered include the following: stochastic analysis on configuration spaces, specifically a mathematically rigorous approach to the stochastic dynamics of Gibbs measures and infinite interacting particle systems; subelliptic PDE, homogenization, and fractals; geometric aspects of Dirichlet forms on metric spaces and function theory on such spaces; generalized harmonic maps as nonlinear analogues of Dirichlet forms, with an emphasis on non-locally compact situations; and a stochastic approach based on Brownian motion to harmonic maps and their regularity. Various new connections between the topics are featured, and it is de...
Nonlinear Least Squares for Inverse Problems
Chavent, Guy
2009-01-01
Presents an introduction into the least squares resolution of nonlinear inverse problems. This title intends to develop a geometrical theory to analyze nonlinear least square (NLS) problems with respect to their quadratic wellposedness, that is, both wellposedness and optimizability
On Dirichlet's Derivation of the Ellipsoid Potential
Dittrich, W
2016-01-01
Newton's potential of a massive homogeneous ellipsoid is derived via Dirichlet's discontinuous factor. At first we review part of Dirichlet's work in an English translation of the original German, and then continue with an extension of his method into the complex plane. With this trick it becomes possible to first calculate the potential and thereafter the force components exerted on a test mass by the ellipsoid. This is remarkable in so far as all other famous researchers prior to Dirichlet merely calculated the attraction components. Unfortunately, Dirichlet's derivation is to a large extent mathematically unacceptable which, however, can be corrected by treating the problem in the complex plane.
A numerical method for finding sign-changing solutions of superlinear Dirichlet problems
Energy Technology Data Exchange (ETDEWEB)
Neuberger, J.M.
1996-12-31
In a recent result it was shown via a variational argument that a class of superlinear elliptic boundary value problems has at least three nontrivial solutions, a pair of one sign and one which sign changes exactly once. These three and all other nontrivial solutions are saddle points of an action functional, and are characterized as local minima of that functional restricted to a codimension one submanifold of the Hilbert space H-0-1-2, or an appropriate higher codimension subset of that manifold. In this paper, we present a numerical Sobolev steepest descent algorithm for finding these three solutions.
Positive solutions of the Dirichlet problem for the prescribed mean curvature equation
Obersnel, Franco; Omari, Pierpaolo
We discuss existence and multiplicity of positive solutions of the prescribed mean curvature problem -div(∇u/√{1+|} )=λf(x,u) in Ω, u=0 on ∂Ω, in a general bounded domain Ω⊂R, depending on the behavior at zero or at infinity of f(x,s), or of its potential F(x,s)=∫0sf(x,t) dt. Our main effort here is to describe, in a way as exhaustive as possible, all configurations of the limits of F(x,s)/s at zero and of F(x,s)/s at infinity, which yield the existence of one, two, three or infinitely many positive solutions. Either strong, or weak, or bounded variation solutions are considered. Our approach is variational and combines critical point theory, the lower and upper solutions method and elliptic regularization.
The virial theorem for nonlinear problems
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Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Blvd 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)], E-mail: paolo.amore@gmail.com, E-mail: fernande@quimica.unlp.edu.ar
2009-09-15
We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular, we consider conservative nonlinear oscillators and obtain the same main result derived earlier from the expansion in Chebyshev polynomials. (letters and comments)
Institute of Scientific and Technical Information of China (English)
SONG Li-mei; WENG Pei-xuan
2012-01-01
In this paper,we study a Dirichlet-type boundary value problem(BVP) of nonlinear fractional differential equation with an order α ∈ (3,4],where the fractional derivative D0α+ is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel'skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results.
Directory of Open Access Journals (Sweden)
P. A. Krutitskii
2012-01-01
Full Text Available The Dirichlet problem for the 2D Helmholtz equation in an exterior domain with cracks is studied. The compatibility conditions at the tips of the cracks are assumed. The existence of a unique classical solution is proved by potential theory. The integral representation for a solution in the form of potentials is obtained. The problem is reduced to the Fredholm equation of the second kind and of index zero, which is uniquely solvable. The asymptotic formulae describing singularities of a solution gradient at the edges (endpoints of the cracks are presented. The weak solution to the problem may not exist, since the problem is studied under such conditions that do not ensure existence of a weak solution.
Toeplitz Operators on Dirichlet Spaces
Institute of Scientific and Technical Information of China (English)
Yu Feng LU; Shun Hua SUN
2001-01-01
In this paper we study Toeplitz operators on Dirichlet spaces and describe the boundedness and compactness of Toeplitz operators on Dirichlet spaces. Meanwhile. we give density theorems for Toeplitz operators on Dirichlet spaces
Studies of Nonlinear Problems. I
Fermi, E.; Pasta, J.; Ulam, S.
1955-05-01
A one-dimensional dynamical system of 64 particles with forces between neighbors containing nonlinear terms has been studied on the Los Alamos computer MANIAC I. The nonlinear terms considered are quadratic, cubic, and broken linear types. The results are analyzed into Fourier components and plotted as a function of time. The results show very little, if any, tendency toward equipartition of energy among the degrees of freedom.
The nonlinear fixed gravimetric boundary value problem
Institute of Scientific and Technical Information of China (English)
于锦海; 朱灼文
1995-01-01
The properly-posedness of the nonlinear fixed gravimetric boundary value problem is shown with the help of nonlinear functional analysis and a new iterative method to solve the problem is also given, where each step of the iterative program is reduced to solving one and the same kind of oblique derivative boundary value problem with the same type. Furthermore, the convergence of the iterative program is proved with Schauder estimate of elliptic differential equation.
1986-04-01
0, p and p will be obtained via elliptic estimates. Assuming that (y,p) is a sufficiently smooth solution of (1.1)-(1.5), we introduce the notations u...equations, in: G. da Prato and G. Geymonat (ed.), Hyperbolicity, Centro Inter- nazionale Matematico Estivo, II ciclo , Cortona 1976, 125-191 .,- [91 S
RESEARCH ON NONLINEAR PROBLEMS IN STRUCTURAL DYNAMICS.
Research on nonlinear problems structural dynamics is briefly summarized. Panel flutter was investigated to make a critical comparison between theory...panel flutter in aerospace vehicles, plausible simplifying assumptions are examined in the light of experimental results. Structural dynamics research
Dirichlet Expression for (1, ) with General Dirichlet Character
Indian Academy of Sciences (India)
V V Rane
2010-02-01
In the famous work of Dirichlet on class number formula, (, ) at =1 has been expressed as a finite sum, where (, ) is the Dirichlet -series of a real Dirichlet character. We show that this expression with obvious modification is valid for the general primitive Dirichlet character .
The role of nonlinearity in inverse problems
Snieder, Roel
1998-06-01
In many practical inverse problems, one aims to retrieve a model that has infinitely many degrees of freedom from a finite amount of data. It follows from a simple variable count that this cannot be done in a unique way. Therefore, inversion entails more than estimating a model: any inversion is not complete without a description of the class of models that is consistent with the data; this is called the appraisal problem. Nonlinearity makes the appraisal problem particularly difficult. The first reason for this is that nonlinear error propagation is a difficult problem. The second reason is that for some nonlinear problems the model parameters affect the way in which the model is being interrogated by the data. Two examples are given of this, and it is shown how the nonlinearity may make the problem more ill-posed. Finally, three attempts are shown to carry out the model appraisal for nonlinear inverse problems that are based on an analytical approach, a numerical approach and a common sense approach.
A Cauchy problem in nonlinear heat conduction
Energy Technology Data Exchange (ETDEWEB)
De Lillo, S [Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Perugia (Italy); Lupo, G [Dipartimento di Matematica e Informatica, Universita degli Studi di Perugia, Via Vanvitelli, 1, 06123 Perugia (Italy); Sanchini, G [Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Perugia (Italy)
2006-06-09
A Cauchy problem on the semiline for a nonlinear diffusion equation is considered, with a boundary condition corresponding to a prescribed thermal conductivity at the origin. The problem is mapped into a moving boundary problem for the linear heat equation with a Robin-type boundary condition. Such a problem is then reduced to a linear integral Volterra equation of II type which admits a unique solution.
Compressed Sensing with Nonlinear Observations and Related Nonlinear Optimisation Problems
Blumensath, Thomas
2012-01-01
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured signals to be sampled far below the rate traditionally prescribed. Nearly all of the theory developed for Compressed Sensing signal recovery assumes that samples are taken using linear measurements. In this paper we instead address the Compressed Sensing recovery problem in a setting where the observations are non-linear. We show that, under conditions similar to those required in the linear setting, the Iterative Hard Thresholding algorithm can be used to accurately recover sparse or structured signals from few non-linear observations. Similar ideas can also be developed in a more general non-linear optimisation framework. In the second part of this paper we therefore present related result that show how this can be done under sparsity and union of subspaces constraints, wh...
Combined algorithms in nonlinear problems of magnetostatics
Energy Technology Data Exchange (ETDEWEB)
Gregus, M.; Khoromsky, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.
1988-05-09
To solve boundary problems of magnetostatics in unbounded two- or three-dimensional regions, we construct combined algorithms based on a combination of the method of boundary integral equations with the grid methods. We study the question of substantiation of the combined method in nonlinear magnetostatic problems without the preliminary discretization of equations and give some results on the convergence of iterative processes that arise in nonlinear cases. We also discuss economical iterative processes and algorithms that solve boundary integral equations on certain surfaces. Finally, examples of numerical solutions of magnetostatic problems that arose when modelling the fields of electrophysical installations are given, too. 14 refs., 2 figs.
Monotone method for nonlinear nonlocal hyperbolic problems
Directory of Open Access Journals (Sweden)
Azmy S. Ackleh
2003-02-01
Full Text Available We present recent results concerning the application of the monotone method for studying existence and uniqueness of solutions to general first-order nonlinear nonlocal hyperbolic problems. The limitations of comparison principles for such nonlocal problems are discussed. To overcome these limitations, we introduce new definitions for upper and lower solutions.
Lobachevsky geometry and modern nonlinear problems
Popov, Andrey
2014-01-01
This monograph presents the basic concepts of hyperbolic Lobachevsky geometry and their possible applications to modern nonlinear applied problems in mathematics and physics, summarizing the findings of roughly the last hundred years. The central sections cover the classical building blocks of hyperbolic Lobachevsky geometry, pseudo spherical surfaces theory, net geometrical investigative techniques of nonlinear differential equations in partial derivatives, and their applications to the analysis of the physical models. As the sine-Gordon equation appears to have profound “geometrical roots” and numerous applications to modern nonlinear problems, it is treated as a universal “object” of investigation, connecting many of the problems discussed. The aim of this book is to form a general geometrical view on the different problems of modern mathematics, physics and natural science in general in the context of non-Euclidean hyperbolic geometry.
Nonlinear elliptic-parabolic problems
Kim, Inwon C
2012-01-01
We introduce a notion of viscosity solutions for a general class of elliptic-parabolic phase transition problems. These include the Richards equation, which is a classical model in filtration theory. Existence and uniqueness results are proved via the comparison principle. In particular, we show existence and stability properties of maximal and minimal viscosity solutions for a general class of initial data. These results are new even in the linear case, where we also show that viscosity solutions coincide with the regular weak solutions introduced in [Alt&Luckhaus 1983].
Advanced Research Workshop on Nonlinear Hyperbolic Problems
Serre, Denis; Raviart, Pierre-Arnaud
1987-01-01
The field of nonlinear hyperbolic problems has been expanding very fast over the past few years, and has applications - actual and potential - in aerodynamics, multifluid flows, combustion, detonics amongst other. The difficulties that arise in application are of theoretical as well as numerical nature. In fact, the papers in this volume of proceedings deal to a greater extent with theoretical problems emerging in the resolution of nonlinear hyperbolic systems than with numerical methods. The volume provides an excellent up-to-date review of the current research trends in this area.
Characterization of the shape stability for nonlinear elliptic problems
Bucur, Dorin
We characterize all geometric perturbations of an open set, for which the solution of a nonlinear elliptic PDE of p-Laplacian type with Dirichlet boundary condition is stable in the L-norm. The necessary and sufficient conditions are jointly expressed by a geometric property associated to the γ-convergence. If the dimension N of the space satisfies N-1
Directory of Open Access Journals (Sweden)
M. D. Mhlongo
2014-01-01
Full Text Available One-dimensional steady-state heat transfer in fins of different profiles is studied. The problem considered satisfies the Dirichlet boundary conditions at one end and the Neumann boundary conditions at the other. The thermal conductivity and heat coefficients are assumed to be temperature dependent, which makes the resulting differential equation highly nonlinear. Classical Lie point symmetry methods are employed, and some reductions are performed. Some invariant solutions are constructed. The effects of thermogeometric fin parameter, the exponent on temperature, and the fin efficiency are studied.
Boundary value problems for partial differential equations with exponential dichotomies
Laederich, Stephane
We are extending the notion of exponential dichotomies to partial differential evolution equations on the n-torus. This allows us to give some simple geometric criteria for the existence of solutions to certain nonlinear Dirichlet boundary value problems.
Topological invariants in nonlinear boundary value problems
Energy Technology Data Exchange (ETDEWEB)
Vinagre, Sandra [Departamento de Matematica, Universidade de Evora, Rua Roma-tilde o Ramalho 59, 7000-671 Evora (Portugal)]. E-mail: smv@uevora.pt; Severino, Ricardo [Departamento de Matematica, Universidade do Minho, Campus de Gualtar, 4710-057 Braga (Portugal)]. E-mail: ricardo@math.uminho.pt; Ramos, J. Sousa [Departamento de Matematica, Instituto Superior Tecnico, Av. Rovisco Pais 1, 1049-001 Lisbon (Portugal)]. E-mail: sramos@math.ist.utl.pt
2005-07-01
We consider a class of boundary value problems for partial differential equations, whose solutions are, basically, characterized by the iteration of a nonlinear function. We apply methods of symbolic dynamics of discrete bimodal maps in the interval in order to give a topological characterization of its solutions.
Recent results and open problems on parabolic equations with gradient nonlinearities
Directory of Open Access Journals (Sweden)
Philippe Souplet
2001-03-01
Full Text Available We survey recent results and present a number of open problems concerning the large-time behavior of solutions of semilinear parabolic equations with gradient nonlinearities. We focus on the model equation with a dissipative gradient term $$u_t-Delta u=u^p-b|abla u|^q,$$ where $p$, $q>1$, $b>0$, with homogeneous Dirichlet boundary conditions. Numerous papers were devoted to this equation in the last ten years, and we compare the results with those known for the case of the pure power reaction-diffusion equation ($b=0$. In presence of the dissipative gradient term a number of new phenomena appear which do not occur when $b=0$. The questions treated concern: sufficient conditions for blowup, behavior of blowing up solutions, global existence and stability, unbounded global solutions, critical exponents, and stationary states.
Algebraic Structure on Dirichlet Spaces
Institute of Scientific and Technical Information of China (English)
Xing FANG; Ping HE; Jian Gang YING
2006-01-01
In this short note, we shall give a few equivalent conditions for a closed form to be Markovian, and prove that the closure of a sub-algebra of bounded functions in a Dirichlet space must be Markovian. We also study the regular representation of Dirichlet spaces and the classification of Dirichlet subspaces.
Multigrid Methods for Nonlinear Problems: An Overview
Energy Technology Data Exchange (ETDEWEB)
Henson, V E
2002-12-23
Since their early application to elliptic partial differential equations, multigrid methods have been applied successfully to a large and growing class of problems, from elasticity and computational fluid dynamics to geodetics and molecular structures. Classical multigrid begins with a two-grid process. First, iterative relaxation is applied, whose effect is to smooth the error. Then a coarse-grid correction is applied, in which the smooth error is determined on a coarser grid. This error is interpolated to the fine grid and used to correct the fine-grid approximation. Applying this method recursively to solve the coarse-grid problem leads to multigrid. The coarse-grid correction works because the residual equation is linear. But this is not the case for nonlinear problems, and different strategies must be employed. In this presentation we describe how to apply multigrid to nonlinear problems. There are two basic approaches. The first is to apply a linearization scheme, such as the Newton's method, and to employ multigrid for the solution of the Jacobian system in each iteration. The second is to apply multigrid directly to the nonlinear problem by employing the so-called Full Approximation Scheme (FAS). In FAS a nonlinear iteration is applied to smooth the error. The full equation is solved on the coarse grid, after which the coarse-grid error is extracted from the solution. This correction is then interpolated and applied to the fine grid approximation. We describe these methods in detail, and present numerical experiments that indicate the efficacy of them.
Pattern selection as a nonlinear eigenvalue problem
Büchel, P
1996-01-01
A unique pattern selection in the absolutely unstable regime of driven, nonlinear, open-flow systems is reviewed. It has recently been found in numerical simulations of propagating vortex structures occuring in Taylor-Couette and Rayleigh-Benard systems subject to an externally imposed through-flow. Unlike the stationary patterns in systems without through-flow the spatiotemporal structures of propagating vortices are independent of parameter history, initial conditions, and system length. They do, however, depend on the boundary conditions in addition to the driving rate and the through-flow rate. Our analysis of the Ginzburg-Landau amplitude equation elucidates how the pattern selection can be described by a nonlinear eigenvalue problem with the frequency being the eigenvalue. Approaching the border between absolute and convective instability the eigenvalue problem becomes effectively linear and the selection mechanism approaches that of linear front propagation. PACS: 47.54.+r,47.20.Ky,47.32.-y,47.20.Ft
Directory of Open Access Journals (Sweden)
V. Rukavishnikov
2014-01-01
Full Text Available The existence and uniqueness of the Rv-generalized solution for the first boundary value problem and a second order elliptic equation with coordinated and uncoordinated degeneracy of input data and with strong singularity solution on all boundary of a two-dimensional domain are established.
A Note on Separable Nonlinear Least Squares Problem
Gharibi, Wajeb
2011-01-01
Separable nonlinear least squares (SNLS)problem is a special class of nonlinear least squares (NLS)problems, whose objective function is a mixture of linear and nonlinear functions. It has many applications in many different areas, especially in Operations Research and Computer Sciences. They are difficult to solve with the infinite-norm metric. In this paper, we give a short note on the separable nonlinear least squares problem, unseparated scheme for NLS, and propose an algorithm for solving mixed linear-nonlinear minimization problem, method of which results in solving a series of least squares separable problems.
OPEN PROBLEM: Some nonlinear challenges in biology
Mosconi, Francesco; Julou, Thomas; Desprat, Nicolas; Sinha, Deepak Kumar; Allemand, Jean-François; Croquette, Vincent; Bensimon, David
2008-08-01
Driven by a deluge of data, biology is undergoing a transition to a more quantitative science. Making sense of the data, building new models, asking the right questions and designing smart experiments to answer them are becoming ever more relevant. In this endeavour, nonlinear approaches can play a fundamental role. The biochemical reactions that underlie life are very often nonlinear. The functional features exhibited by biological systems at all levels (from the activity of an enzyme to the organization of a colony of ants, via the development of an organism or a functional module like the one responsible for chemotaxis in bacteria) are dynamically robust. They are often unaffected by order of magnitude variations in the dynamical parameters, in the number or concentrations of actors (molecules, cells, organisms) or external inputs (food, temperature, pH, etc). This type of structural robustness is also a common feature of nonlinear systems, exemplified by the fundamental role played by dynamical fixed points and attractors and by the use of generic equations (logistic map, Fisher-Kolmogorov equation, the Stefan problem, etc.) in the study of a plethora of nonlinear phenomena. However, biological systems differ from these examples in two important ways: the intrinsic stochasticity arising from the often very small number of actors and the role played by evolution. On an evolutionary time scale, nothing in biology is frozen. The systems observed today have evolved from solutions adopted in the past and they will have to adapt in response to future conditions. The evolvability of biological system uniquely characterizes them and is central to biology. As the great biologist T Dobzhansky once wrote: 'nothing in biology makes sense except in the light of evolution'.
Some Duality Results for Fuzzy Nonlinear Programming Problem
Sangeeta Jaiswal; Geetanjali Panda
2012-01-01
The concept of duality plays an important role in optimization theory. This paper discusses some relations between primal and dual nonlinear programming problems in fuzzy environment. Here, fuzzy feasible region for a general fuzzy nonlinear programming is formed and the concept of fuzzy feasible solution is defined. First order dual relation for fuzzy nonlinear programming problem is studied.
On the convergence of nonlinear Beltrami type operators
Directory of Open Access Journals (Sweden)
Riccardo De Arcangelis
1986-11-01
Full Text Available One of the results proved is the following: if (fh is a sequence of K-quasiregular mappings, converging to f in L1loc , whose jacobians verify a weak integrability condition, then the solutions of Dirichlet problems for the nonlinear Laplace-Beltrami operator associated to each fh converge to the solution of the Dirichlet problem for the nonlinear Laplace-Beltrami operator associated to f. Such result is deduced as a particular case of a more general theorem concerning nonlinear operators. The case of K-quasiconformal functions fh is also treated. A class of weighted Sobolev spaces associated to quasiconformal mappings is studied.
Bayesian nonlinear regression for large small problems
Chakraborty, Sounak
2012-07-01
Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. This is known as large p small n problem. Furthermore, the problem is more complicated when we have multiple correlated responses. We develop multivariate nonlinear regression models in this setup for accurate prediction. In this paper, we introduce a full Bayesian support vector regression model with Vapnik\\'s ε-insensitive loss function, based on reproducing kernel Hilbert spaces (RKHS) under the multivariate correlated response setup. This provides a full probabilistic description of support vector machine (SVM) rather than an algorithm for fitting purposes. We have also introduced a multivariate version of the relevance vector machine (RVM). Instead of the original treatment of the RVM relying on the use of type II maximum likelihood estimates of the hyper-parameters, we put a prior on the hyper-parameters and use Markov chain Monte Carlo technique for computation. We have also proposed an empirical Bayes method for our RVM and SVM. Our methods are illustrated with a prediction problem in the near-infrared (NIR) spectroscopy. A simulation study is also undertaken to check the prediction accuracy of our models. © 2012 Elsevier Inc.
An Algorithm to Solve Separable Nonlinear Least Square Problem
Directory of Open Access Journals (Sweden)
Wajeb Gharibi
2013-07-01
Full Text Available Separable Nonlinear Least Squares (SNLS problem is a special class of Nonlinear Least Squares (NLS problems, whose objective function is a mixture of linear and nonlinear functions. SNLS has many applications in several areas, especially in the field of Operations Research and Computer Science. Problems related to the class of NLS are hard to resolve having infinite-norm metric. This paper gives a brief explanation about SNLS problem and offers a Lagrangian based algorithm for solving mixed linear-nonlinear minimization problem
The fully nonlinear stratified geostrophic adjustment problem
Coutino, Aaron; Stastna, Marek
2017-01-01
The study of the adjustment to equilibrium by a stratified fluid in a rotating reference frame is a classical problem in geophysical fluid dynamics. We consider the fully nonlinear, stratified adjustment problem from a numerical point of view. We present results of smoothed dam break simulations based on experiments in the published literature, with a focus on both the wave trains that propagate away from the nascent geostrophic state and the geostrophic state itself. We demonstrate that for Rossby numbers in excess of roughly 2 the wave train cannot be interpreted in terms of linear theory. This wave train consists of a leading solitary-like packet and a trailing tail of dispersive waves. However, it is found that the leading wave packet never completely separates from the trailing tail. Somewhat surprisingly, the inertial oscillations associated with the geostrophic state exhibit evidence of nonlinearity even when the Rossby number falls below 1. We vary the width of the initial disturbance and the rotation rate so as to keep the Rossby number fixed, and find that while the qualitative response remains consistent, the Froude number varies, and these variations are manifested in the form of the emanating wave train. For wider initial disturbances we find clear evidence of a wave train that initially propagates toward the near wall, reflects, and propagates away from the geostrophic state behind the leading wave train. We compare kinetic energy inside and outside of the geostrophic state, finding that for long times a Rossby number of around one-quarter yields an equal split between the two, with lower (higher) Rossby numbers yielding more energy in the geostrophic state (wave train). Finally we compare the energetics of the geostrophic state as the Rossby number varies, finding long-lived inertial oscillations in the majority of the cases and a general agreement with the past literature that employed either hydrostatic, shallow-water equation-based theory or
Institute of Scientific and Technical Information of China (English)
郭秀清; 王旭焕
2013-01-01
讨论了分数阶Langevin方程的非局部狄利克雷边值问题,利用Leray-Schauder's和压缩映像原理,分别得到了方程的解的存在及唯一性.%In this paper,a new type of Langevin equation with fractional orders with Nonlocal Dirichlet Boundary Value Problems is considered.By using Leray-Schauder's fixed point theorem and Banach's contraction mapping principle,we obtain the existence and uniqueness results of the solution.
Studies in nonlinear problems of energy
Matkowsky, B. J.
1992-07-01
Emphasis has been on combustion and flame propagation. The research program was on modeling, analysis and computation of combustion phenomena, with emphasis on transition from laminar to turbulent combustion. Nonlinear dynamics and pattern formation were investigated in the transition. Stability of combustion waves, and transitions to complex waves are described. Combustion waves possess large activation energies, so that chemical reactions are significant only in thin layers, or reaction zones. In limit of infinite activation energy, the zones shrink to moving surfaces, termed fronts which must be found during the analysis, so that the problems are moving free boundary problems. The studies are carried out for limiting case with fronts, while the numerical studies are carried out for finite, though large, activation energy. Accurate resolution of the solution in the reaction zones is essential, otherwise false predictions of dynamics are possible. Since the the reaction zones move, adaptive pseudo-spectral methods were developed. The approach is based on a synergism of analytical and computational methods. The numerical computations build on and extend the analytical information. Furthermore, analytical solutions serve as benchmarks for testing the accuracy of the computation. Finally, ideas from analysis (singular perturbation theory) have induced new approaches to computations. The computational results suggest new analysis to be considered. Among the recent interesting results, was spatio-temporal chaos in combustion. One goal is extension of the adaptive pseudo-spectral methods to adaptive domain decomposition methods. Efforts have begun to develop such methods for problems with multiple reaction zones, corresponding to problems with more complex, and more realistic chemistry. Other topics included stochastics, oscillators, Rysteretic Josephson junctions, DC SQUID, Markov jumps, laser with saturable absorber, chemical physics, Brownian movement, combustion
Studies in nonlinear problems of energy
Energy Technology Data Exchange (ETDEWEB)
Matkowsky, B.J.
1992-07-01
Emphasis has been on combustion and flame propagation. The research program was on modeling, analysis and computation of combustion phenomena, with emphasis on transition from laminar to turbulent combustion. Nonlinear dynamics and pattern formation were investigated in the transition. Stability of combustion waves, and transitions to complex waves are described. Combustion waves possess large activation energies, so that chemical reactions are significant only in thin layers, or reaction zones. In limit of infinite activation energy, the zones shrink to moving surfaces, (fronts) which must be found during the analysis, so that (moving free boundary problems). The studies are carried out for limiting case with fronts, while the numerical studies are carried out for finite, though large, activation energy. Accurate resolution of the solution in the reaction zones is essential, otherwise false predictions of dynamics are possible. Since the the reaction zones move, adaptive pseudo-spectral methods were developed. The approach is based on a synergism of analytical and computational methods. The numerical computations build on and extend the analytical information. Furthermore, analytical solutions serve as benchmarks for testing the accuracy of the computation. Finally, ideas from analysis (singular perturbation theory) have induced new approaches to computations. The computational results suggest new analysis to be considered. Among the recent interesting results, was spatio-temporal chaos in combustion. One goal is extension of the adaptive pseudo-spectral methods to adaptive domain decomposition methods. Efforts have begun to develop such methods for problems with multiple reaction zones, corresponding to problems with more complex, and more realistic chemistry. Other topics included stochastics, oscillators, Rysteretic Josephson junctions, DC SQUID, Markov jumps, laser with saturable absorber, chemical physics, Brownian movement, combustion synthesis, etc.
A NEW SMOOTHING EQUATIONS APPROACH TO THE NONLINEAR COMPLEMENTARITY PROBLEMS
Institute of Scientific and Technical Information of China (English)
Chang-feng Ma; Pu-yan Nie; Guo-ping Liang
2003-01-01
The nonlinear complementarity problem can be reformulated as a nonsmooth equation. In this paper we propose a new smoothing Newton algorithm for the solution of the nonlinear complementarity problem by constructing a new smoothing approximation function. Global and local superlinear convergence results of the algorithm are obtained under suitable conditions. Numerical experiments confirm the good theoretical properties of the algorithm.
Nonlinear algebraic multigrid for constrained solid mechanics problems using Trilinos
Gee, M.W.; R. S. Tuminaro
2012-01-01
The application of the finite element method to nonlinear solid mechanics problems results in the neccessity to repeatedly solve a large nonlinear set of equations. In this paper we limit ourself to problems arising in constrained solid mechanics problems. It is common to apply some variant of Newton?s method or a Newton? Krylov method to such problems. Often, an analytic Jacobian matrix is formed and used in the above mentioned methods. However, if no analytic Jacobian is given, Newton metho...
Bifurcation of solutions of nonlinear Sturm–Liouville problems
Directory of Open Access Journals (Sweden)
Gulgowski Jacek
2001-01-01
Full Text Available A global bifurcation theorem for the following nonlinear Sturm–Liouville problem is given Moreover we give various versions of existence theorems for boundary value problems The main idea of these proofs is studying properties of an unbounded connected subset of the set of all nontrivial solutions of the nonlinear spectral problem , associated with the boundary value problem , in such a way that .
Multisplitting for linear, least squares and nonlinear problems
Energy Technology Data Exchange (ETDEWEB)
Renaut, R.
1996-12-31
In earlier work, presented at the 1994 Iterative Methods meeting, a multisplitting (MS) method of block relaxation type was utilized for the solution of the least squares problem, and nonlinear unconstrained problems. This talk will focus on recent developments of the general approach and represents joint work both with Andreas Frommer, University of Wupertal for the linear problems and with Hans Mittelmann, Arizona State University for the nonlinear problems.
Fast discriminative latent Dirichlet allocation
National Aeronautics and Space Administration — This is the code for fast discriminative latent Dirichlet allocation, which is an algorithm for topic modeling and text classification. The related paper is at...
Diophantine approximation and Dirichlet series
Queffélec, Hervé
2013-01-01
This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...
DBEM crack propagation for nonlinear fracture problems
Directory of Open Access Journals (Sweden)
R. Citarella
2015-10-01
Full Text Available A three-dimensional crack propagation simulation is performed by the Dual Boundary Element Method (DBEM. The Stress Intensity Factors (SIFs along the front of a semi elliptical crack, initiated from the external surface of a hollow axle, are calculated for bending and press fit loading separately and for a combination of them. In correspondence of the latter loading condition, a crack propagation is also simulated, with the crack growth rates calculated using the NASGRO3 formula, calibrated for the material under analysis (steel ASTM A469. The J-integral and COD approaches are selected for SIFs calculation in DBEM environment, where the crack path is assessed by the minimum strain energy density criterion (MSED. In correspondence of the initial crack scenario, SIFs along the crack front are also calculated by the Finite Element (FE code ZENCRACK, using COD, in order to provide, by a cross comparison with DBEM, an assessment on the level of accuracy obtained. Due to the symmetry of the bending problem a pure mode I crack propagation is realised with no kinking of the propagating crack whereas for press fit loading the crack propagation becomes mixed mode. The crack growth analysis is nonlinear because of normal gap elements used to model the press fit condition with added friction, and is developed in an iterative-incremental procedure. From the analysis of the SIFs results related to the initial cracked configuration, it is possible to assess the impact of the press fit condition when superimposed to the bending load case.
LINEARIZATION AND CORRECTION METHOD FOR NONLINEAR PROBLEMS
Institute of Scientific and Technical Information of China (English)
何吉欢
2002-01-01
A new perturbation-like technique called linearization and correction method is proposed. Contrary to the traditional perturbation techniques, the present theory does not assume that the solution is expressed in the form of a power series of small parameter. To obtain an asymptotic solution of nonlinear system, the technique first searched for a solution for the linearized system, then a correction was added to the linearized solution. So the obtained results are uniformly valid for both weakly and strongly nonlinear equations.
Remarks on a benchmark nonlinear constrained optimization problem
Institute of Scientific and Technical Information of China (English)
Luo Yazhong; Lei Yongjun; Tang Guojin
2006-01-01
Remarks on a benchmark nonlinear constrained optimization problem are made. Due to a citation error, two absolutely different results for the benchmark problem are obtained by independent researchers. Parallel simulated annealing using simplex method is employed in our study to solve the benchmark nonlinear constrained problem with mistaken formula and the best-known solution is obtained, whose optimality is testified by the Kuhn-Tucker conditions.
Ruofeng Rao; Zhilin Pu; Shouming Zhong; Jialin Huang
2013-01-01
By the way of Lyapunov-Krasovskii functional approach and some variational methods in the Sobolev space ${W}_{0}^{1,p}\\left(Ω\\right)$ , a global asymptotical stability criterion for p-Laplace partial differential equations with partial fuzzy parameters is derived under Dirichlet boundary condition, which gives a positive answer to an open problem proposed in some related literatures. Different from many previous related literatures, the nonlinear p-Laplace diffusion item plays its role in the...
Minimax theory for a class of nonlinear statistical inverse problems
Ray, Kolyan; Schmidt-Hieber, Johannes
2016-06-01
We study a class of statistical inverse problems with nonlinear pointwise operators motivated by concrete statistical applications. A two-step procedure is proposed, where the first step smoothes the data and inverts the nonlinearity. This reduces the initial nonlinear problem to a linear inverse problem with deterministic noise, which is then solved in a second step. The noise reduction step is based on wavelet thresholding and is shown to be minimax optimal (up to logarithmic factors) in a pointwise function-dependent sense. Our analysis is based on a modified notion of Hölder smoothness scales that are natural in this setting.
A Null Space Approach for Solving Nonlinear Complementarity Problems
Institute of Scientific and Technical Information of China (English)
Pu-yan Nie
2006-01-01
In this work, null space techniques are employed to tackle nonlinear complementarity problems(NCPs). NCP conditions are transform into a nonlinear programming problem, which is handled by null space algorithms. The NCP conditions are divided into two groups. Some equalities and inequalities in an NCP are treated as constraints. While other equalities and inequalities in an NCP are to be regarded as objective function.Two groups are all updated in every step. Null space approaches are extended to nonlinear complementarity problems. Two different solvers are employed for an NCP in an algorithm.
A Numerical Embedding Method for Solving the Nonlinear Optimization Problem
Institute of Scientific and Technical Information of China (English)
田保锋; 戴云仙; 孟泽红; 张建军
2003-01-01
A numerical embedding method was proposed for solving the nonlinear optimization problem. By using the nonsmooth theory, the existence and the continuation of the following path for the corresponding homotopy equations were proved. Therefore the basic theory for the algorithm of the numerical embedding method for solving the non-linear optimization problem was established. Based on the theoretical results, a numerical embedding algorithm was designed for solving the nonlinear optimization problem, and prove its convergence carefully. Numerical experiments show that the algorithm is effective.
Robust Monotone Iterates for Nonlinear Singularly Perturbed Boundary Value Problems
Directory of Open Access Journals (Sweden)
Boglaev Igor
2009-01-01
Full Text Available This paper is concerned with solving nonlinear singularly perturbed boundary value problems. Robust monotone iterates for solving nonlinear difference scheme are constructed. Uniform convergence of the monotone methods is investigated, and convergence rates are estimated. Numerical experiments complement the theoretical results.
Analytical Solutions to Non-linear Mechanical Oscillation Problems
DEFF Research Database (Denmark)
Kaliji, H. D.; Ghadimi, M.; Barari, Amin
2011-01-01
In this paper, the Max-Min Method is utilized for solving the nonlinear oscillation problems. The proposed approach is applied to three systems with complex nonlinear terms in their motion equations. By means of this method, the dynamic behavior of oscillation systems can be easily approximated u...
A Unified Approach for Solving Nonlinear Regular Perturbation Problems
Khuri, S. A.
2008-01-01
This article describes a simple alternative unified method of solving nonlinear regular perturbation problems. The procedure is based upon the manipulation of Taylor's approximation for the expansion of the nonlinear term in the perturbed equation. An essential feature of this technique is the relative simplicity used and the associated unified…
Finite Element Analysis to Two-Dimensional Nonlinear Sloshing Problems
Institute of Scientific and Technical Information of China (English)
严承华; 王赤忠; 程尔升
2001-01-01
A two-dimensional nonlinear sloshing problem is analyzed by means of the fully nonlinear theory and time domainsecond order theory of water waves. Liquid sloshing in a rectangular container subjected to a horizontal excitation is sim-ulated by the finite element method. Comparisons between the two theories are made based on their numerical results. Itis found that good agreement is obtained for the case of small amplitude oscillation and obvious differences occur forlarge amplitude excitation. Even though, the second order solution can still exhibit typical nonlinear features ofnonlinear wave and can be used instead of the fully nonlinear theory.
QUASILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS WITH DISCONTINUOUS NONLINEARITIES
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In this paper we shall consider a discontinuous nonlinear nonmonotone elliptic boundary value problem, i.e. a quasilinear elliptic hemivariational inequality. This kind of problems is strongly motivated by various problems in mechanics. By use of the notion of the generalized gradient of Clarke and the theory of pseudomonotone operators, we will prove the existence of solutions.
Inverse Coefficient Problems for Nonlinear Elliptic Variational Inequalities
Institute of Scientific and Technical Information of China (English)
Run-sheng Yang; Yun-hua Ou
2011-01-01
This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic variational inequalities. The unknown coefficient of elliptic variational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic variational inequalities is unique solvable for the given class of coefficients. The existence of quasisolutions of the inverse problems is obtained.
Modified Filled Function to Solve NonlinearProgramming Problem
Institute of Scientific and Technical Information of China (English)
2015-01-01
Filled function method is an approach to find the global minimum of nonlinear functions. Many Problems, such as computing,communication control, and management, in real applications naturally result in global optimization formulations in a form ofnonlinear global integer programming. This paper gives a modified filled function method to solve the nonlinear global integerprogramming problem. The properties of the proposed modified filled function are also discussed in this paper. The results ofpreliminary numerical experiments are also reported.
Iterative regularization methods for nonlinear ill-posed problems
Scherzer, Otmar; Kaltenbacher, Barbara
2008-01-01
Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.
Nonlinear eigenvalue problems with semipositone structure
Directory of Open Access Journals (Sweden)
Alfonso Castro
2000-10-01
Full Text Available In this paper we summarize the developments of semipositone problems to date, including very recent results on semipositone systems. We also discuss applications and open problems.
Inverse Problems for Nonlinear Delay Systems
2011-03-15
Ba82]. For nonlinear delay systems such as those discussed here, approximation in the context of a linear semigroup framework as presented [BBu1, BBu2...linear part generates a linear semigroup as in [BBu1, BBu2, BKap]. One then uses the linear semigroup in a vari- ation of parameters implicit...BBu2, BKap] (for the linear semigroup ) plus a Gronwall inequality. An alternative (and more general) approach given in [Ba82] eschews use of the Trotter
Parabolic Perturbation of a Nonlinear Hyperbolic Problem Arising in Physiology
Colli, P.; Grasselli, M.
We study a transport-diffusion initial value problem where the diffusion codlicient is "small" and the transport coefficient is a time function depending on the solution in a nonlinear and nonlocal way. We show the existence and the uniqueness of a weak solution of this problem. Moreover we discuss its asymptotic behaviour as the diffusion coefficient goes to zero, obtaining a well-posed first-order nonlinear hyperbolic problem. These problems arise from mathematical models of muscle contraction in the framework of the sliding filament theory.
THIRD-ORDER NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
王国灿; 金丽
2002-01-01
Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established.Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained.The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.
Higher-order techniques for some problems of nonlinear control
Directory of Open Access Journals (Sweden)
Sarychev Andrey V.
2002-01-01
Full Text Available A natural first step when dealing with a nonlinear problem is an application of some version of linearization principle. This includes the well known linearization principles for controllability, observability and stability and also first-order optimality conditions such as Lagrange multipliers rule or Pontryagin's maximum principle. In many interesting and important problems of nonlinear control the linearization principle fails to provide a solution. In the present paper we provide some examples of how higher-order methods of differential geometric control theory can be used for the study nonlinear control systems in such cases. The presentation includes: nonlinear systems with impulsive and distribution-like inputs; second-order optimality conditions for bang–bang extremals of optimal control problems; methods of high-order averaging for studying stability and stabilization of time-variant control systems.
Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems
Vázquez, Luis
2013-01-01
Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems explores how Newton's equation for the motion of one particle in classical mechanics combined with finite difference methods allows creation of a mechanical scenario to solve basic problems in linear algebra and programming. The authors present a novel, unified numerical and mechanical approach and an important analysis method of optimization. This book also: Presents mechanical method for determining matrix singularity or non-independence of dimension and complexity Illustrates novel mathematical applications of classical Newton’s law Offers a new approach and insight to basic, standard problems Includes numerous examples and applications Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems is an ideal book for undergraduate and graduate students as well as researchers interested in linear problems and optimization, and nonlinear dynamics.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
With the aid of a nonlinear transformation, a class of nonlinear convectiondiffusion PDE in one space dimension is converted into a linear one, the unique solution of a nonlinear boundary-initial value problem for the nonlinear PDE can be exactly expressed by the nonlinear transformation, and several illustrative examples are given
DEFICIENT FUNCTIONS OF RANDOM DIRICHLET SERIES
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this article, the uniqueness theorem of Dirichlet series is proved. Then the random Dirichlet series in the right half plane is studied, and the result that the random Dirichlet series of finite order has almost surely(a.s.) no deficient functions is proved.
Studies in nonlinear problems of energy
Energy Technology Data Exchange (ETDEWEB)
Matkowsky, B.J.
1990-11-01
We carry out a research program with primary emphasis on the applications of Bifurcation and Stability Theory to Problems of energy, with specific emphasis on Problems of Combustion and Flame Propagation. In particular we consider the problem of transition from laminar to turbulent flame propagation. A great deal of progress has been made in our investigations. More than one hundred and thirty papers citing this project have been prepared for publication in technical journals. A list of the papers, including abstracts for each paper, is appended to this report.
Nonlinear Preserver Problems on B(H)
Institute of Scientific and Technical Information of China (English)
Jian Lian CUI
2011-01-01
Let H be a complex Hilbert space of dimension greater than 2, and B(H) denote the Banach algebra of all bounded linear operators on H. For A, B ∈ B(H), define the binary relation A ≤* B by A*A = A*B and AA* = AB*. Then (B(H), "≤*") is a partially ordered set and the relation "≤*" is called the star order on B(H). Denote by Bs(H) the set of all self-adjoint operators in B(H). In this paper, we first characterize nonlinear continuous bijective maps on Bs (H) which preserve the star order in both directions. We characterize also additive maps (or linear maps) on B(H) (or nest algebras) which are multiplicative at some invertible operator.
Andreani, Roberto; Friedlander, Ana; Mello, Margarida P.; Santos, Sandra A.
2005-06-01
In this work we show that the mixed nonlinear complementarity problem may be formulated as an equivalent nonlinear bound-constrained optimization problem that preserves the smoothness of the original data. One may thus take advantage of existing codes for bound-constrained optimization. This approach is implemented and tested by means of an extensive set of numerical experiments, showing promising results. The mixed nonlinear complementarity problems considered in the tests arise from the discretization of a motion planning problem concerning a set of rigid 3D bodies in contact in the presence of friction. We solve the complementarity problem associated with a single time frame, thus calculating the contact forces and accelerations of the bodies involved.
An Adaptive Neural Network Model for Nonlinear Programming Problems
Institute of Scientific and Technical Information of China (English)
Xiang-sun Zhang; Xin-jian Zhuo; Zhu-jun Jing
2002-01-01
In this paper a canonical neural network with adaptively changing synaptic weights and activation function parameters is presented to solve general nonlinear programming problems. The basic part of the model is a sub-network used to find a solution of quadratic programming problems with simple upper and lower bounds. By sequentially activating the sub-network under the control of an external computer or a special analog or digital processor that adjusts the weights and parameters, one then solves general nonlinear programming problems. Convergence proof and numerical results are given.
Variational approach to various nonlinear problems in geometry and physics
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this survey, we will summarize the existence results of nonlinear partial differential equations which arises from geometry or physics by using variational method. We use the method to study Kazdan-Warner problem, Chern-Simons-Higgs model, Toda systems, and the prescribed Q-curvature problem in 4-dimension.
On a Highly Nonlinear Self-Obstacle Optimal Control Problem
Energy Technology Data Exchange (ETDEWEB)
Di Donato, Daniela, E-mail: daniela.didonato@unitn.it [University of Trento, Department of Mathematics (Italy); Mugnai, Dimitri, E-mail: dimitri.mugnai@unipg.it [Università di Perugia, Dipartimento di Matematica e Informatica (Italy)
2015-10-15
We consider a non-quadratic optimal control problem associated to a nonlinear elliptic variational inequality, where the obstacle is the control itself. We show that, fixed a desired profile, there exists an optimal solution which is not far from it. Detailed characterizations of the optimal solution are given, also in terms of approximating problems.
A Hybrid Method for Nonlinear Least Squares Problems
Institute of Scientific and Technical Information of China (English)
Zhongyi Liu; Linping Sun
2007-01-01
A negative curvature method is applied to nonlinear least squares problems with indefinite Hessian approximation matrices. With the special structure of the method,a new switch is proposed to form a hybrid method. Numerical experiments show that this method is feasible and effective for zero-residual,small-residual and large-residual problems.
Toeplitz Algebras on Dirichlet Spaces
Institute of Scientific and Technical Information of China (English)
TAN Yan-hua; WANG Xiao-feng
2001-01-01
In the present paper, some properties of Toeplitz algebras on Dirichlet spaces for several complex variables are discussed; in particular, the automorphism group of the Toeplitz C* -algebra, (C1), generated by Toeplitz operators with C1-symbols is discussed. In addition, the first cohomology group of (C1) is computed.
On the Dirichlet's Box Principle
Poon, Kin-Keung; Shiu, Wai-Chee
2008-01-01
In this note, we will focus on several applications on the Dirichlet's box principle in Discrete Mathematics lesson and number theory lesson. In addition, the main result is an innovative game on a triangular board developed by the authors. The game has been used in teaching and learning mathematics in Discrete Mathematics and some high schools in…
Multigrid Reduction in Time for Nonlinear Parabolic Problems
Energy Technology Data Exchange (ETDEWEB)
Falgout, R. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Manteuffel, T. A. [Univ. of Colorado, Boulder, CO (United States); O' Neill, B. [Univ. of Colorado, Boulder, CO (United States); Schroder, J. B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-01-04
The need for parallel-in-time is being driven by changes in computer architectures, where future speed-ups will be available through greater concurrency, but not faster clock speeds, which are stagnant.This leads to a bottleneck for sequential time marching schemes, because they lack parallelism in the time dimension. Multigrid Reduction in Time (MGRIT) is an iterative procedure that allows for temporal parallelism by utilizing multigrid reduction techniques and a multilevel hierarchy of coarse time grids. MGRIT has been shown to be effective for linear problems, with speedups of up to 50 times. The goal of this work is the efficient solution of nonlinear problems with MGRIT, where efficient is defined as achieving similar performance when compared to a corresponding linear problem. As our benchmark, we use the p-Laplacian, where p = 4 corresponds to a well-known nonlinear diffusion equation and p = 2 corresponds to our benchmark linear diffusion problem. When considering linear problems and implicit methods, the use of optimal spatial solvers such as spatial multigrid imply that the cost of one time step evaluation is fixed across temporal levels, which have a large variation in time step sizes. This is not the case for nonlinear problems, where the work required increases dramatically on coarser time grids, where relatively large time steps lead to worse conditioned nonlinear solves and increased nonlinear iteration counts per time step evaluation. This is the key difficulty explored by this paper. We show that by using a variety of strategies, most importantly, spatial coarsening and an alternate initial guess to the nonlinear time-step solver, we can reduce the work per time step evaluation over all temporal levels to a range similar with the corresponding linear problem. This allows for parallel scaling behavior comparable to the corresponding linear problem.
A reduced order model for nonlinear vibroacoustic problems
Directory of Open Access Journals (Sweden)
Ouisse Morvan
2012-07-01
Full Text Available This work is related to geometrical nonlinearities applied to thin plates coupled with fluid-filled domain. Model reduction is performed to reduce the computation time. Reduced order model (ROM is issued from the uncoupled linear problem and enriched with residues to describe the nonlinear behavior and coupling effects. To show the efficiency of the proposed method, numerical simulations in the case of an elastic plate closing an acoustic cavity are presented.
Frozen Landweber Iteration for Nonlinear Ill-Posed Problems
Institute of Scientific and Technical Information of China (English)
J.Xu; B.Han; L.Li
2007-01-01
In this paper we propose a modification of the Landweber iteration termed frozen Landweber iteration for nonlinear ill-posed problems.A convergence analysis for this iteration is presented.The numerical performance of this frozen Landweber iteration for a nonlinear Hammerstein integral equation is compared with that of the Landweber iteration.We obtain a shorter running time of the frozen Landweber iteration based on the same convergence accuracy.
Numerical Simulation of Two-dimensional Nonlinear Sloshing Problems
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Numerical simulation of a two-dimensional nonlinearsloshing problem is preceded by the finite element method. Two theories are used. One is fully nonlinear theory; the other is time domain second order theory. A liquid sloshing in a rectangular container subjected to a horizontal excitation is simulated using these two theories. Numerical results are obtained and comparisons are made. It is found that a good agreement is obtained for the case of small amplitude oscillation. For the situation of large amplitude excitation, although the differences between using the two theories are obvious the second order solution can still exhibit typical nonlinear features of nonlinear wave.
Inverse Coefficient Problems for Nonlinear Parabolic Differential Equations
Institute of Scientific and Technical Information of China (English)
Yun Hua OU; Alemdar HASANOV; Zhen Hai LIU
2008-01-01
This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation.The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible coefficients.It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence.Based on this result the existence of a quasisolution of the inverse problem is obtained in the appropriate class of admissible coefficients.
Energy Technology Data Exchange (ETDEWEB)
Kong Dexing [Department of Mathematics, Zhejiang University, Hangzhou 310027 (China); Sun Qingyou, E-mail: qysun@cms.zju.edu.cn [Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027 (China)
2011-04-01
All articles must In this paper we introduce some new concepts for second-order hyperbolic equations: two-point boundary value problem, global exact controllability and exact controllability. For several kinds of important linear and nonlinear wave equations arising from physics and geometry, we prove the existence of smooth solutions of the two-point boundary value problems and show the global exact controllability of these wave equations. In particular, we investigate the two-point boundary value problem for one-dimensional wave equation defined on a closed curve and prove the existence of smooth solution which implies the exact controllability of this kind of wave equation. Furthermore, based on this, we study the two-point boundary value problems for the wave equation defined on a strip with Dirichlet or Neumann boundary conditions and show that the equation still possesses the exact controllability in these cases. Finally, as an application, we introduce the hyperbolic curvature flow and obtain a result analogous to the well-known theorem of Gage and Hamilton for the curvature flow of plane curves.
Interval Arithmetic for Nonlinear Problem Solving
2013-01-01
Implementation of interval arithmetic in complex problems has been hampered by the tedious programming exercise needed to develop a particular implementation. In order to improve productivity, the use of interval mathematics is demonstrated using the computing platform INTLAB that allows for the development of interval-arithmetic-based programs more efficiently than with previous interval-arithmetic libraries. An interval-Newton Generalized-Bisection (IN/GB) method is developed in this platfo...
On a stochastic Burgers equation with Dirichlet boundary conditions
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Ekaterina T. Kolkovska
2003-01-01
Full Text Available We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.
Analysis of nonlinear channel friction inverse problem
Institute of Scientific and Technical Information of China (English)
CHENG Weiping; LIU Guohua
2007-01-01
Based on the Backus-Gilbert inverse theory, the singular value decomposition (SVD) for general inverse matrices and the optimization algorithm are used to solve the channel friction inverse problem. The resolution and covari- ance friction inverse model in matrix form is developed to examine the reliability of solutions. Theoretical analyses demonstrate that the convergence rate of the general Newton optimization algorithm is in the second-order. The Wiggins method is also incorporated into the algorithm. Using the method, noise can be suppressed effectively, and the results are close to accurate solutions with proper control parameters. Also, the numerical stability can be improved.
A Smoothing Inexact Newton Method for Generalized Nonlinear Complementarity Problem
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Meixia Li
2012-01-01
Full Text Available Based on the smoothing function of penalized Fischer-Burmeister NCP-function, we propose a new smoothing inexact Newton algorithm with non-monotone line search for solving the generalized nonlinear complementarity problem. We view the smoothing parameter as an independent variable. Under suitable conditions, we show that any accumulation point of the generated sequence is a solution of the generalized nonlinear complementarity problem. We also establish the local superlinear (quadratic convergence of the proposed algorithm under the BD-regular assumption. Preliminary numerical experiments indicate the feasibility and efficiency of the proposed algorithm.
Institute of Scientific and Technical Information of China (English)
LI; Shujie
2001-01-01
［1］Martin Schecher,The Fucik spectrum,Indiana University Mathematics Journal,1994,43(4):1139-1157.［2］Dancer,E.N.,Remarks on jumping nonlinearities,in Topics in Nonlinear Analysis (eds.Escher,Simonett),Basel:Birkhauser,1999,101-116.［3］Dancer,E.N.,Du Yihong,Existence of changing sign solutions for semilinear problems with jumping nonlinearities at zero,Proceedings of the Royal Society of Edinburgh,1994,124A:1165-1176.［4］Dancer,E.N.,Du Yihong,Multiple solutions of some semilinear elliptic equations via generalized conley index,Journal of Mathematical Analysis and Applications,1995,189:848-871.［5］Li Shujie,Zhang Zhitao,Sign-changing solutions and multiple solutions theorems for semilinear elliptic boundary value problems with jumping nonlinearities,Acta Mathematica Sinica,2000,16(1):113-122.［6］Chang Kung-ching,Li Shujie,Liu Jiaquan,Remarks on multiple solutions for asymptotically linear elliptic boundary value problems.Topological methods for Nonlinear Analysis,Journal of the Juliusz Schauder Center,1994,3:179-187.［7］Alfonso Castro,Jorge Cossio,Multiple solutions for a nonlinear Dirichlet problem,SIAM J.Math.Anal.,1994,25(6):1554-1561.［8］Alfonso Castro,Jorge Cossio,John M.Neuberger,A sign-changing solution for a superlinear Dirichlet problem,Rocky Mountain J.M.,1997,27:1041-1053.［9］Alfonso Castro,Jorge Cossio,John M.Neuberger,A minimax principle,index of the critical point,and existence of sign-changing solutions to Elliptic boundary value problems,E.J.Diff.Eqn.,1998 (2):1-18.［10］Thomas Bartsch,Wang Zhiqiang,On the existence of sign-changing solutions for semilinear Dirichlet problems,Topological Methods in Nonlinear Analysis,Journal of the Juliusz Schauder Center,1996,(7):115-131.［11］Li Shujie,Zhang Zhitao,Multiple solutions theorems for semilinear elliptic boundary value problems with resonance at infinity,Discrete and Continuous Dynamical System,1999,5(3):489-493.［12］Mawhin,J.,Willem,M.,Critical Point Theory and
Bonus algorithm for large scale stochastic nonlinear programming problems
Diwekar, Urmila
2015-01-01
This book presents the details of the BONUS algorithm and its real world applications in areas like sensor placement in large scale drinking water networks, sensor placement in advanced power systems, water management in power systems, and capacity expansion of energy systems. A generalized method for stochastic nonlinear programming based on a sampling based approach for uncertainty analysis and statistical reweighting to obtain probability information is demonstrated in this book. Stochastic optimization problems are difficult to solve since they involve dealing with optimization and uncertainty loops. There are two fundamental approaches used to solve such problems. The first being the decomposition techniques and the second method identifies problem specific structures and transforms the problem into a deterministic nonlinear programming problem. These techniques have significant limitations on either the objective function type or the underlying distributions for the uncertain variables. Moreover, these ...
Directory of Open Access Journals (Sweden)
Ruofeng Rao
2013-01-01
Full Text Available By the way of Lyapunov-Krasovskii functional approach and some variational methods in the Sobolev space W01,p(Ω, a global asymptotical stability criterion for p-Laplace partial differential equations with partial fuzzy parameters is derived under Dirichlet boundary condition, which gives a positive answer to an open problem proposed in some related literatures. Different from many previous related literatures, the nonlinear p-Laplace diffusion item plays its role in the new criterion though the nonlinear p-Laplace presents great difficulties. Moreover, numerical examples illustrate that our new stability criterion can judge what the previous criteria cannot do.
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this article, we consider the existence of local and global solution to the Cauchy problem of a doubly nonlinear equation. By introducing the norms |||f|||h and
Generative supervised classification using Dirichlet process priors.
Davy, Manuel; Tourneret, Jean-Yves
2010-10-01
Choosing the appropriate parameter prior distributions associated to a given bayesian model is a challenging problem. Conjugate priors can be selected for simplicity motivations. However, conjugate priors can be too restrictive to accurately model the available prior information. This paper studies a new generative supervised classifier which assumes that the parameter prior distributions conditioned on each class are mixtures of Dirichlet processes. The motivations for using mixtures of Dirichlet processes is their known ability to model accurately a large class of probability distributions. A Monte Carlo method allowing one to sample according to the resulting class-conditional posterior distributions is then studied. The parameters appearing in the class-conditional densities can then be estimated using these generated samples (following bayesian learning). The proposed supervised classifier is applied to the classification of altimetric waveforms backscattered from different surfaces (oceans, ices, forests, and deserts). This classification is a first step before developing tools allowing for the extraction of useful geophysical information from altimetric waveforms backscattered from nonoceanic surfaces.
Galerkin approximations of nonlinear optimal control problems in Hilbert spaces
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Mickael D. Chekroun
2017-07-01
Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.
Solution of Contact Problems for Nonlinear Gao Beam and Obstacle
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J. Machalová
2015-01-01
Full Text Available Contact problem for a large deformed beam with an elastic obstacle is formulated, analyzed, and numerically solved. The beam model is governed by a nonlinear fourth-order differential equation developed by Gao, while the obstacle is considered as the elastic foundation of Winkler’s type in some distance under the beam. The problem is static without a friction and modeled either using Signorini conditions or by means of normal compliance contact conditions. The problems are then reformulated as optimal control problems which is useful both for theoretical aspects and for solution methods. Discretization is based on using the mixed finite element method with independent discretization and interpolations for foundation and beam elements. Numerical examples demonstrate usefulness of the presented solution method. Results for the nonlinear Gao beam are compared with results for the classical Euler-Bernoulli beam model.
INITIAL BOUNDARY VALUE PROBLEM FOR A DAMPED NONLINEAR HYPERBOLIC EQUATION
Institute of Scientific and Technical Information of China (English)
陈国旺
2003-01-01
In the paper, the existence and uniqueness of the generalized global solution and the classical global solution of the initial boundary value problems for the nonlinear hyperbolic equationare proved by Galerkin method and the sufficient conditions of blow-up of solution in finite time are given.
Major open problems in chaos theory and nonlinear dynamics
Li, Y Charles
2013-01-01
Nowadays, chaos theory and nonlinear dynamics lack research focuses. Here we mention a few major open problems: 1. an effective description of chaos and turbulence, 2. rough dependence on initial data, 3. arrow of time, 4. the paradox of enrichment, 5. the paradox of pesticides, 6. the paradox of plankton.
Linear iterative technique for solution of nonlinear thermal network problems
Energy Technology Data Exchange (ETDEWEB)
Seabourn, C.M.
1976-11-01
A method for rapid and accurate solution of linear and/or nonlinear thermal network problems is described. It is a matrix iterative process that converges for nodal temperatures and variations of thermal conductivity with temperature. The method is computer oriented and can be changed easily for design studies.
A POSITIVE INTERIOR-POINT ALGORITHM FOR NONLINEAR COMPLEMENTARITY PROBLEMS
Institute of Scientific and Technical Information of China (English)
马昌凤; 梁国平; 陈新美
2003-01-01
A new iterative method, which is called positive interior-point algorithm, is presented for solving the nonlinear complementarity problems. This method is of the desirable feature of robustness. And the convergence theorems of the algorithm is established. In addition, some numerical results are reported.
Multiple solutions for inhomogeneous nonlinear elliptic problems arising in astrophyiscs
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Marco Calahorrano
2004-04-01
Full Text Available Using variational methods we prove the existence and multiplicity of solutions for some nonlinear inhomogeneous elliptic problems on a bounded domain in $mathbb{R}^n$, with $ngeq 2$ and a smooth boundary, and when the domain is $mathbb{R}_+^n$
Some problems on nonlinear hyperbolic equations and applications
Peng, YueJun
2010-01-01
This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.
Adomian decomposition method for nonlinear Sturm-Liouville problems
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Sennur Somali
2007-09-01
Full Text Available In this paper the Adomian decomposition method is applied to the nonlinear Sturm-Liouville problem-y" + y(tp=λy(t, y(t > 0, t ∈ I = (0, 1, y(0 = y(1 = 0, where p > 1 is a constant and λ > 0 is an eigenvalue parameter. Also, the eigenvalues and the behavior of eigenfuctions of the problem are demonstrated.
Modified constrained differential evolution for solving nonlinear global optimization problems
2013-01-01
Nonlinear optimization problems introduce the possibility of multiple local optima. The task of global optimization is to find a point where the objective function obtains its most extreme value while satisfying the constraints. Some methods try to make the solution feasible by using penalty function methods, but the performance is not always satisfactory since the selection of the penalty parameters for the problem at hand is not a straightforward issue. Differential evolut...
WEIGHTED COMPOSITION OPERATORS BETWEEN DIRICHLET SPACES
Institute of Scientific and Technical Information of China (English)
Wang Maofa
2011-01-01
In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.
Iterative total variation schemes for nonlinear inverse problems
Bachmayr, Markus; Burger, Martin
2009-10-01
In this paper we discuss the construction, analysis and implementation of iterative schemes for the solution of inverse problems based on total variation regularization. Via different approximations of the nonlinearity we derive three different schemes resembling three well-known methods for nonlinear inverse problems in Hilbert spaces, namely iterated Tikhonov, Levenberg-Marquardt and Landweber. These methods can be set up such that all arising subproblems are convex optimization problems, analogous to those appearing in image denoising or deblurring. We provide a detailed convergence analysis and appropriate stopping rules in the presence of data noise. Moreover, we discuss the implementation of the schemes and the application to distributed parameter estimation in elliptic partial differential equations.
Quantum "violation" of Dirichlet boundary condition
Park, I. Y.
2017-02-01
Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a tension between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum-corrected black hole solution of the 1PI action no longer obeys, in the naive manner one may expect, the Dirichlet boundary conditions imposed at the classical level. We attribute the 'violation' of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.
Quantum violation of Dirichlet boundary condition
Park, I Y
2016-01-01
Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a clash between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum corrected solution of the 1PI action no longer obeys the Dirichlet boundary conditions imposed at the classical level. We attribute the violation of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.
Microscopic structures from reduction of continuum nonlinear problems
Lovison, Alberto
2011-01-01
We present an application of the Amann-Zehnder exact finite reduction to a class of nonlinear perturbations of elliptic elasto-static problems. We propose the existence of minmax solutions by applying Ljusternik-Schnirelmann theory to a finite dimensional variational formulation of the problem, based on a suitable spectral cut-off. As a by-product, with a choice of fit variables, we establish a variational equivalence between the above spectral finite description and a discrete mechanical model. By doing so, we decrypt the abstract information encoded in the AZ reduction and give rise to a concrete and finite description of the continuous problem.
Numerical solution of control problems governed by nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Heinkenschloss, M. [Virginia Polytechnic Institute and State Univ., Blacksburg, VA (United States)
1994-12-31
In this presentation the author investigates an iterative method for the solution of optimal control problems. These problems are formulated as constrained optimization problems with constraints arising from the state equation and in the form of bound constraints on the control. The method for the solution of these problems uses the special structure of the problem arising from the bound constraint and the state equation. It is derived from SQP methods and projected Newton methods and combines the advantages of both methods. The bound constraint is satisfied by all iterates using a projection, the nonlinear state equation is satisfied in the limit. Only a linearized state equation has to be solved in every iteration. The solution of the linearized problems are done using multilevel methods and GMRES.
A monomial chaos approach for efficient uncertainty quantification on nonlinear problems
Witteveen, J.A.S.; Bijl, H.
2008-01-01
A monomial chaos approach is presented for efficient uncertainty quantification in nonlinear computational problems. Propagating uncertainty through nonlinear equations can be computationally intensive for existing uncertainty quantification methods. It usually results in a set of nonlinear equation
A monomial chaos approach for efficient uncertainty quantification on nonlinear problems
Witteveen, J.A.S.; Bijl, H.
2008-01-01
A monomial chaos approach is presented for efficient uncertainty quantification in nonlinear computational problems. Propagating uncertainty through nonlinear equations can be computationally intensive for existing uncertainty quantification methods. It usually results in a set of nonlinear
Lu, Bao-Liang; Ito, Koji
2003-09-01
In this paper we present a method for converting general nonlinear programming (NLP) problems into separable programming (SP) problems by using feedforward neural networks (FNNs). The basic idea behind the method is to use two useful features of FNNs: their ability to approximate arbitrary continuous nonlinear functions with a desired degree of accuracy and their ability to express nonlinear functions in terms of parameterized compositions of functions of single variables. According to these two features, any nonseparable objective functions and/or constraints in NLP problems can be approximately expressed as separable functions with FNNs. Therefore, any NLP problems can be converted into SP problems. The proposed method has three prominent features. (a) It is more general than existing transformation techniques; (b) it can be used to formulate optimization problems as SP problems even when their precise analytic objective function and/or constraints are unknown; (c) the SP problems obtained by the proposed method may highly facilitate the selection of grid points for piecewise linear approximation of nonlinear functions. We analyze the computational complexity of the proposed method and compare it with an existing transformation approach. We also present several examples to demonstrate the method and the performance of the simplex method with the restricted basis entry rule for solving SP problems.
Higher order Nevanlinna functions and the inverse three spectra problem
Directory of Open Access Journals (Sweden)
Olga Boyko
2016-01-01
Full Text Available The three spectra problem of recovering the Sturm-Liouville equation by the spectrum of the Dirichlet-Dirichlet boundary value problem on \\([0,a]\\, the Dirichlet-Dirichlet problem on \\([0,a/2]\\ and the Neumann-Dirichlet problem on \\([a/2,a]\\ is considered. Sufficient conditions of solvability and of uniqueness of the solution to such a problem are found.
Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.
Lectures on nonlinear evolution equations initial value problems
Racke, Reinhard
2015-01-01
This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value p...
Franck, I M
2014-01-01
This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an optimization problem in an appropriately selected family of distributions. The goal is two-fold. Firstly, to find lower-dimensional representations of the unknown parameter vector that capture as much as possible of the associated posterior density, and secondly to enable the computation of the approximate posterior density with as few forward calls as possible. We discuss how these objectives can be achieved by using a fully Bayesian argumentation and employing the marginal likelihood or evidence as the ultimate model validation metric for any proposed dimensionality reduction. We demonstrate the performance of the proposed methodology to problems in nonlinear elastography where the identification of the mechanical properties of biological materials can inform non-invasive, ...
On a mixed problem for a coupled nonlinear system
Directory of Open Access Journals (Sweden)
Marcondes R. Clark
1997-03-01
Full Text Available In this article we prove the existence and uniqueness of solutions to the mixed problem associated with the nonlinear system $$ u_{tt}-M(int_Omega |abla u|^2dxDelta u+|u|^ ho u+heta =f $$ $$ heta _t -Delta heta +u_{t}=g $$ where $M$ is a positive real function, and $f$ and $g$ are known real functions.
On Nonlinear Approximations to Cosmic Problems with Mixed Boundary Conditions
Mancinelli, Paul J.; Yahil, Amos; Ganon, Galit; Dekel, Avishai
1993-01-01
Nonlinear approximations to problems with mixed boundary conditions are useful for predicting large-scale streaming velocities from the density field, or vice-versa. We evaluate the schemes of Bernardeau \\cite{bernardeau92}, Gramann \\cite{gramann93}, and Nusser \\etal \\cite{nusser91}, using smoothed density and velocity fields obtained from $N$-body simulations of a CDM universe. The approximation of Nusser \\etal is overall the most accurate and robust. For Gaussian smoothing of 1000\\kms\\ the ...
Application of homotopy analysis method for solving nonlinear Cauchy problem
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V.G. Gupta
2012-11-01
Full Text Available In this paper, by means of the homotopy analysis method (HAM, the solutions of some nonlinear Cauchy problem of parabolic-hyperbolic type are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter \\hbar that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear examples to obtain the exact solutions. The results reveal that the proposed method is very effective and simple.
Dirichlet Form of Product of Variational Fractals
Institute of Scientific and Technical Information of China (English)
刘源
2003-01-01
Much effort has gone into constructing Dirichlet forms to define Laplacians on self-similar sets. However, the results have only been successful on p.c.f. (post critical finite) fractals. We prove the existence of a Dirichlet form on a class of non-p.c.f. sets that are the product of variational fractals.
A convergence theory for a class of nonlinear programming problems.
Rauch, S. W.
1973-01-01
A recent convergence theory of Elkin concerning methods for unconstrained minimization is extended to a certain class of nonlinear programming problems. As in Elkin's original approach, the analysis of a variety of step-length algorithms is treated entirely separately from that of several direction algorithms. This allows for their combination into many different methods for solving the constrained problem. These include some of the methods of Rosen and Zoutendijk. We also extend the results of Topkis and Veinott to nonconvex sets and drop their requirement of the uniform feasibility of a subsequence of the search directions.
A New Superlinearly Convergent SQP Algorithm for Nonlinear Minimax Problems
Institute of Scientific and Technical Information of China (English)
Jin-bao Jian; Ran Quan; Qing-jie Hu
2007-01-01
In this paper, the nonlinear minimax problems are discussed. By means of the Sequential Quadratic Programming (SQP), a new descent algorithm for solving the problems is presented. At each iteration of the proposed algorithm, a main search direction is obtained by solving a Quadratic Programming (QP) which always has a solution. In order to avoid the Maratos effect, a correction direction is obtained by updating the main direction with a simple explicit formula. Under mild conditions without the strict complementarity, the global and superlinear convergence of the algorithm can be obtained. Finally, some numerical experiments are reported.
An Algorithm for Linearly Constrained Nonlinear Programming Programming Problems.
1980-01-01
ALGORITHM FOR LINEARLY CONSTRAINED NONLINEAR PROGRAMMING PROBLEMS Mokhtar S. Bazaraa and Jamie J. Goode In this paper an algorithm for solving a linearly...distance pro- gramr.ing, as in the works of Bazaraa and Goode 12], and Wolfe [16 can be used for solving this problem. Special methods that take advantage of...34 Pacific Journal of Mathematics, Volume 16, pp. 1-3, 1966. 2. M. S. Bazaraa and J. j. Goode, "An Algorithm for Finding the Shortest Element of a
Properties of positive solutions to a nonlinear parabolic problem
Institute of Scientific and Technical Information of China (English)
2007-01-01
This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vazquez and the comparison principle, we deduce that the blow-up occurs only on the boundary (?)Ω. In addition, for a bounded Lipschitz domainΩ, we establish the blow-up rate estimates for the positive solution to this problem with a= 0.
Meta-analysis using Dirichlet process.
Muthukumarana, Saman; Tiwari, Ram C
2016-02-01
This article develops a Bayesian approach for meta-analysis using the Dirichlet process. The key aspect of the Dirichlet process in meta-analysis is the ability to assess evidence of statistical heterogeneity or variation in the underlying effects across study while relaxing the distributional assumptions. We assume that the study effects are generated from a Dirichlet process. Under a Dirichlet process model, the study effects parameters have support on a discrete space and enable borrowing of information across studies while facilitating clustering among studies. We illustrate the proposed method by applying it to a dataset on the Program for International Student Assessment on 30 countries. Results from the data analysis, simulation studies, and the log pseudo-marginal likelihood model selection procedure indicate that the Dirichlet process model performs better than conventional alternative methods.
Directory of Open Access Journals (Sweden)
Abaker. A. Hassaballa.
2015-10-01
Full Text Available - In recent years, many more of the numerical methods were used to solve a wide range of mathematical, physical, and engineering problems linear and nonlinear. This paper applies the homotopy perturbation method (HPM to find exact solution of partial differential equation with the Dirichlet and Neumann boundary conditions.
Inverse problem for multi-body interaction of nonlinear waves
Marruzzo, Alessia; Antenucci, Fabrizio; Pagnani, Andrea; Leuzzi, Luca
2016-01-01
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we test two methods based on pseudolikelihood, respectively with regularization and with decimation, to determine the coupling constants from sets of measured configurations. We test statistical inference predictions for increasing number of sampled configurations and for an externally tunable {\\em temperature}-like parameter mimicing real data noise and helping minimization procedures. Analyzed models with phasors and rotors are generalizations of problems of real-valued spherical problems (e.g., density fluctuations), discrete spins (Ising and vectorial Potts) or finite number of states (standard Potts): inference methods presented here can, then, be straightforward applied to a large class of inverse problems.
Toeplitz Operators on Dirichlet-Type Space of Unit Ball
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Jin Xia
2014-01-01
Full Text Available We construct a function u in L2Bn, dV which is unbounded on any neighborhood of each boundary point of Bn such that Toeplitz operator Tu is a Schatten p-class 0
Dirichlet-type space DBn, dV. Then, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Dirichlet-type space DBn, dV. We determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator. We investigate the zero-product problem for several Toeplitz operators with radial symbols. Furthermore, the corresponding commuting problem of Toeplitz operators whose symbols are of the form ξku is studied, where k ∈ Zn, ξ ∈ ∂Bn, and u is a radial function.
Chen, Yun; Yang, Hui
2016-12-01
In the era of big data, there are increasing interests on clustering variables for the minimization of data redundancy and the maximization of variable relevancy. Existing clustering methods, however, depend on nontrivial assumptions about the data structure. Note that nonlinear interdependence among variables poses significant challenges on the traditional framework of predictive modeling. In the present work, we reformulate the problem of variable clustering from an information theoretic perspective that does not require the assumption of data structure for the identification of nonlinear interdependence among variables. Specifically, we propose the use of mutual information to characterize and measure nonlinear correlation structures among variables. Further, we develop Dirichlet process (DP) models to cluster variables based on the mutual-information measures among variables. Finally, orthonormalized variables in each cluster are integrated with group elastic-net model to improve the performance of predictive modeling. Both simulation and real-world case studies showed that the proposed methodology not only effectively reveals the nonlinear interdependence structures among variables but also outperforms traditional variable clustering algorithms such as hierarchical clustering.
Chen, Yun; Yang, Hui
2016-12-14
In the era of big data, there are increasing interests on clustering variables for the minimization of data redundancy and the maximization of variable relevancy. Existing clustering methods, however, depend on nontrivial assumptions about the data structure. Note that nonlinear interdependence among variables poses significant challenges on the traditional framework of predictive modeling. In the present work, we reformulate the problem of variable clustering from an information theoretic perspective that does not require the assumption of data structure for the identification of nonlinear interdependence among variables. Specifically, we propose the use of mutual information to characterize and measure nonlinear correlation structures among variables. Further, we develop Dirichlet process (DP) models to cluster variables based on the mutual-information measures among variables. Finally, orthonormalized variables in each cluster are integrated with group elastic-net model to improve the performance of predictive modeling. Both simulation and real-world case studies showed that the proposed methodology not only effectively reveals the nonlinear interdependence structures among variables but also outperforms traditional variable clustering algorithms such as hierarchical clustering.
Global Optimization of Nonlinear Blend-Scheduling Problems
Directory of Open Access Journals (Sweden)
Pedro A. Castillo Castillo
2017-04-01
Full Text Available The scheduling of gasoline-blending operations is an important problem in the oil refining industry. This problem not only exhibits the combinatorial nature that is intrinsic to scheduling problems, but also non-convex nonlinear behavior, due to the blending of various materials with different quality properties. In this work, a global optimization algorithm is proposed to solve a previously published continuous-time mixed-integer nonlinear scheduling model for gasoline blending. The model includes blend recipe optimization, the distribution problem, and several important operational features and constraints. The algorithm employs piecewise McCormick relaxation (PMCR and normalized multiparametric disaggregation technique (NMDT to compute estimates of the global optimum. These techniques partition the domain of one of the variables in a bilinear term and generate convex relaxations for each partition. By increasing the number of partitions and reducing the domain of the variables, the algorithm is able to refine the estimates of the global solution. The algorithm is compared to two commercial global solvers and two heuristic methods by solving four examples from the literature. Results show that the proposed global optimization algorithm performs on par with commercial solvers but is not as fast as heuristic approaches.
Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem
Directory of Open Access Journals (Sweden)
R. J. Moitsheki
2012-01-01
Full Text Available We consider the one-dimensional steady fin problem with the Dirichlet boundary condition at one end and the Neumann boundary condition at the other. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. We perform preliminary group classification to determine forms of the arbitrary functions appearing in the considered equation for which the principal Lie algebra is extended. Some invariant solutions are constructed. The effects of thermogeometric fin parameter and the exponent on temperature are studied. Also, the fin efficiency is analyzed.
2002-06-01
IEEE TRANSACTIONS ON AUTOMATIC CONTROL , VOL. 47, NO. 6, JUNE 2002 1033 Application of Optimization Techniques to a Nonlinear Problem of Communication... IEEE TRANSACTIONS ON AUTOMATIC CONTROL , VOL. 47, NO. 6, JUNE 2002 We consider J source-destination pairs, each of which is assigned a fixed multihop...blocking probabilities are at the maximum permitted value. IEEE TRANSACTIONS ON AUTOMATIC CONTROL , VOL. 47, NO. 6, JUNE
The relative degree enhancement problem for MIMO nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Schoenwald, D.A. [Oak Ridge National Lab., TN (United States); Oezguener, Ue. [Ohio State Univ., Columbus, OH (United States). Dept. of Electrical Engineering
1995-07-01
The authors present a result for linearizing a nonlinear MIMO system by employing partial feedback - feedback at all but one input-output channel such that the SISO feedback linearization problem is solvable at the remaining input-output channel. The partial feedback effectively enhances the relative degree at the open input-output channel provided the feedback functions are chosen to satisfy relative degree requirements. The method is useful for nonlinear systems that are not feedback linearizable in a MIMO sense. Several examples are presented to show how these feedback functions can be computed. This strategy can be combined with decentralized observers for a completely decentralized feedback linearization result for at least one input-output channel.
Lavrentiev regularization method for nonlinear ill-posed problems
Kinh, N V
2002-01-01
In this paper we shall be concerned with Lavientiev regularization method to reconstruct solutions x sub 0 of non ill-posed problems F(x)=y sub o , where instead of y sub 0 noisy data y subdelta is an element of X with absolut(y subdelta-y sub 0) X is an accretive nonlinear operator from a real reflexive Banach space X into itself. In this regularization method solutions x subalpha supdelta are obtained by solving the singularly perturbed nonlinear operator equation F(x)+alpha(x-x*)=y subdelta with some initial guess x*. Assuming certain conditions concerning the operator F and the smoothness of the element x*-x sub 0 we derive stability estimates which show that the accuracy of the regularized solutions is order optimal provided that the regularization parameter alpha has been chosen properly.
Nonlinear programming for classification problems in machine learning
Astorino, Annabella; Fuduli, Antonio; Gaudioso, Manlio
2016-10-01
We survey some nonlinear models for classification problems arising in machine learning. In the last years this field has become more and more relevant due to a lot of practical applications, such as text and web classification, object recognition in machine vision, gene expression profile analysis, DNA and protein analysis, medical diagnosis, customer profiling etc. Classification deals with separation of sets by means of appropriate separation surfaces, which is generally obtained by solving a numerical optimization model. While linear separability is the basis of the most popular approach to classification, the Support Vector Machine (SVM), in the recent years using nonlinear separating surfaces has received some attention. The objective of this work is to recall some of such proposals, mainly in terms of the numerical optimization models. In particular we tackle the polyhedral, ellipsoidal, spherical and conical separation approaches and, for some of them, we also consider the semisupervised versions.
Jacobi elliptic functions: A review of nonlinear oscillatory application problems
Kovacic, Ivana; Cveticanin, Livija; Zukovic, Miodrag; Rakaric, Zvonko
2016-10-01
This review paper is concerned with the applications of Jacobi elliptic functions to nonlinear oscillators whose restoring force has a monomial or binomial form that involves cubic and/or quadratic nonlinearity. First, geometric interpretations of three basic Jacobi elliptic functions are given and their characteristics are discussed. It is shown then how their different forms can be utilized to express exact solutions for the response of certain free conservative oscillators. These forms are subsequently used as a starting point for a presentation of different quantitative techniques for obtaining an approximate response for free perturbed nonlinear oscillators. An illustrative example is provided. Further, two types of externally forced nonlinear oscillators are reviewed: (i) those that are excited by elliptic-type excitations with different exact and approximate solutions; (ii) those that are damped and excited by harmonic excitations, but their approximate response is expressed in terms of Jacobi elliptic functions. Characteristics of the steady-state response are discussed and certain qualitative differences with respect to the classical Duffing oscillator excited harmonically are pointed out. Parametric oscillations of the oscillators excited by an elliptic-type forcing are considered as well, and the differences with respect to the stability chart of the classical Mathieu equation are emphasized. The adjustment of the Melnikov method to derive the general condition for the onset of homoclinic bifurcations in a system parametrically excited by an elliptic-type forcing is provided and compared with those corresponding to harmonic excitations. Advantages and disadvantages of the use of Jacobi elliptic functions in nonlinear oscillatory application problems are discussed and some suggestions for future work are given.
Application of genetic algorithms in nonlinear heat conduction problems.
Kadri, Muhammad Bilal; Khan, Waqar A
2014-01-01
Genetic algorithms are employed to optimize dimensionless temperature in nonlinear heat conduction problems. Three common geometries are selected for the analysis and the concept of minimum entropy generation is used to determine the optimum temperatures under the same constraints. The thermal conductivity is assumed to vary linearly with temperature while internal heat generation is assumed to be uniform. The dimensionless governing equations are obtained for each selected geometry and the dimensionless temperature distributions are obtained using MATLAB. It is observed that GA gives the minimum dimensionless temperature in each selected geometry.
Nonlinear triple-point problems on time scales
Directory of Open Access Journals (Sweden)
Douglas R. Anderson
2004-04-01
Full Text Available We establish the existence of multiple positive solutions to the nonlinear second-order triple-point boundary-value problem on time scales, $$displaylines{ u^{Delta abla}(t+h(tf(t,u(t=0, cr u(a=alpha u(b+delta u^Delta(a,quad eta u(c+gamma u^Delta(c=0 }$$ for $tin[a,c]subsetmathbb{T}$, where $mathbb{T}$ is a time scale, $eta, gamma, deltage 0$ with $Beta+gamma>0$, $0
Basis properties of eigenfunctions of nonlinear Sturm-Liouville problems
Peter E. Zhidkov
2000-01-01
We consider three nonlinear eigenvalue problems that consist of $$-y''+f(y^2)y=lambda y$$ with one of the following boundary conditions: $$displaylines{ y(0)=y(1)=0 quad y'(0)=p ,,cr y'(0)=y(1)=0 quad y(0)=p,, cr y'(0)=y'(1)=0 quad y(0)=p,, }$$ where $p$ is a positive constant. Under smoothness and monotonicity conditions on $f$, we show the existence and uniqueness of a sequence of eigenvalues ${lambda _n}$ and corresponding eigenfunctions ${y_n}$ such that $y_n(x)$ has precisely $n$ roots i...
Computer-aided analysis of nonlinear problems in transport phenomena
Brown, R. A.; Scriven, L. E.; Silliman, W. J.
1980-01-01
The paper describes algorithms for equilibrium and steady-state problems with coefficients in the expansions derived by the Galerkin weighted residual method and calculated from the resulting sets of nonlinear algebraic equations by the Newton-Raphson method. Initial approximations are obtained from nearby solutions by continuation techniques as parameters are varied. The Newton-Raphson technique is preferred because the Jacobian of the solution is useful for continuation, for analyzing the stability of solutions, for detecting bifurcation of solution families, and for computing asymptotic estimates of the effects on any solution of small changes in parameters, boundary conditions, and boundary shape.
On extensions of local Dirichlet forms
Robinson, Derek W.
2016-01-01
Let $\\ce$ be a Dirichlet form on $L_2(X\\,;\\mu)$ where $(X,\\mu)$ is locally compact $\\sigma$-compact measure space. Assume $\\ce$ is inner regular, i.e.\\ regular in restriction to functions of compact support, and local in the sense that $\\ce(\\varphi,\\psi)=0$ for all $\\varphi, \\psi\\in D(\\ce)$ with $\\varphi\\,\\psi=0$. We construct two Dirichlet forms $\\ce_m$ and $\\ce_M$ such that $\\ce_m\\leq \\ce\\leq \\ce_M$. These forms are potentially the smallest and largest such Dirichlet forms. In particular $\\...
Hierarchical topic modeling with nested hierarchical Dirichlet process
Institute of Scientific and Technical Information of China (English)
Yi-qun DING; Shan-ping LI; Zhen ZHANG; Bin SHEN
2009-01-01
This paper deals with the statistical modeling of latent topic hierarchies in text corpora. The height of the topic tree is assumed as fixed, while the number of topics on each level as unknown a priori and to be inferred from data. Taking a nonparametric Bayesian approach to this problem, we propose a new probabilistic generative model based on the nested hierarchical Dirichlet process (nHDP) and present a Markov chain Monte Carlo sampling algorithm for the inference of the topic tree structure as welt as the word distribution of each topic and topic distribution of each document. Our theoretical analysis and experiment results show that this model can produce a more compact hierarchical topic structure and captures more free-grained topic relationships compared to the hierarchical latent Dirichlet allocation model.
Global properties of Dirichlet forms on discrete spaces
Schmidt, Marcel
2012-01-01
The goal of this Diploma thesis is to study global properties of Dirichlet forms associated with infinite weighted graphs. These include recurrence and transience, stochastic completeness and the question whether the Neumann form on a graph is regular. We show that recurrence of the regular Dirichlet form of a graph is equivalent to recurrence of a certain random walk on it. After that, we prove some general characterizations of the mentioned global properties which allow us to investigate their connections. It turns out that recurrence always implies stochastic completeness and the regularity of the Neumann form. In the case where the underlying $\\ell^2$-space has finite measure, we are able to show that all concepts coincide. Finally, we demonstrate that the above properties are all equivalent to uniqueness of solutions to the eigenvalue problem for the (unbounded) graph Laplacian when considered on the right space.
Approximation on computing partial sum of nonlinear differential eigenvalue problems
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In computing the electronic structure and energy band in a system of multi-particles, quite a large number of problems are referred to the acquisition of obtaining the partial sum of densities and energies using the “first principle”. In the conventional method, the so-called self-consistency approach is limited to a small scale because of high computing complexity. In this paper, the problem of computing the partial sum for a class of nonlinear differential eigenvalue equations is changed into the constrained functional minimization. By space decomposition and perturbation method, a secondary approximating formula for the minimal is provided. It is shown that this formula is more precise and its quantity of computation can be reduced significantly
Directory of Open Access Journals (Sweden)
Ky Ho
2014-11-01
Full Text Available We establish sufficient conditions for the existence of multiple positive solutions to nonautonomous quasilinear elliptic equations with p(x-Laplacian and sign-changing nonlinearity. For solving the Dirichlet boundary-value problem we use variational and topological methods. The nonexistence of positive solutions is also studied.
On the linear properties of the nonlinear radiative transfer problem
Pikichyan, H. V.
2016-11-01
In this report, we further expose the assertions made in nonlinear problem of reflection/transmission of radiation from a scattering/absorbing one-dimensional anisotropic medium of finite geometrical thickness, when both of its boundaries are illuminated by intense monochromatic radiative beams. The new conceptual element of well-defined, so-called, linear images is noteworthy. They admit a probabilistic interpretation. In the framework of nonlinear problem of reflection/transmission of radiation, we derive solution which is similar to linear case. That is, the solution is reduced to the linear combination of linear images. By virtue of the physical meaning, these functions describe the reflectivity and transmittance of the medium for a single photon or their beam of unit intensity, incident on one of the boundaries of the layer. Thereby the medium in real regime is still under the bilateral illumination by external exciting radiation of arbitrary intensity. To determine the linear images, we exploit three well known methods of (i) adding of layers, (ii) its limiting form, described by differential equations of invariant imbedding, and (iii) a transition to the, so-called, functional equations of the "Ambartsumyan's complete invariance".
Boundary-Value Problems for Weakly Nonlinear Delay Differential Systems
Directory of Open Access Journals (Sweden)
A. Boichuk
2011-01-01
Full Text Available Conditions are derived of the existence of solutions of nonlinear boundary-value problems for systems of n ordinary differential equations with constant coefficients and single delay (in the linear part and with a finite number of measurable delays of argument in nonlinearity: ż(t=Az(t-τ+g(t+εZ(z(hi(t,t,ε, t∈[a,b], assuming that these solutions satisfy the initial and boundary conditions z(s:=ψ(s if s∉[a,b], lz(⋅=α∈Rm. The use of a delayed matrix exponential and a method of pseudoinverse by Moore-Penrose matrices led to an explicit and analytical form of sufficient conditions for the existence of solutions in a given space and, moreover, to the construction of an iterative process for finding the solutions of such problems in a general case when the number of boundary conditions (defined by a linear vector functional l does not coincide with the number of unknowns in the differential system with a single delay.
Dirichlet boundary value problem with variable growth
Institute of Scientific and Technical Information of China (English)
董增福; 付永强
2004-01-01
In this paper, we study higher order elliptic partial differential equations with variable growth, and obtain the existence of solutions in the setting of W'n,p(χ) spaces by means of an abstract result for variational inequalities obtained by Gossez and Mustonen. Our result generalizes the corresponding one of Kovacik and Rakosntk.
Estimation in Dirichlet random effects models
Kyung, Minjung; Casella, George; 10.1214/09-AOS731
2010-01-01
We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the multinomial and Dirichlet distributions, and is shown to be an improvement, in terms of operator norm and efficiency, over other commonly used MCMC algorithms. We also investigate methods for the estimation of the precision parameter of the Dirichlet process, finding that maximum likelihood may not be desirable, but a posterior mode is a reasonable approach. Examples are given to show how these models perform on real data. Our results complement both the theoretical basis of the Dirichlet process nonparametric prior and the computational work that has been done to date.
Application of HPEM to investigate the response and stability of nonlinear problems in vibration
DEFF Research Database (Denmark)
Mohammadi, M.H.; Mohammadi, A.; Kimiaeifar, A.;
2010-01-01
In this work, a powerful analytical method, called He's Parameter Expanding Methods (HPEM) is used to obtain the exact solution of nonlinear problems in nonlinear vibration. In this work, the governing equation is obtained by using Lagrange method, then the nonlinear governing equation is solved...... and convenient for solving these problems....
An inverse problem of determining a nonlinear term in an ordinary differential equation
Kamimura, Yutaka
1998-01-01
An inverse problem for a nonlinear ordinary differential equation is discussed. We prove an existence theorem of a nonlinear term with which a boundary value problem admits a solution. This is an improvement of earlier work by A. Lorenzi. We also prove a uniqueness theorem of the nonlinear term.
FDM for Elliptic Equations with Bitsadze-Samarskii-Dirichlet Conditions
Directory of Open Access Journals (Sweden)
Allaberen Ashyralyev
2012-01-01
Full Text Available A numerical method is proposed for solving nonlocal boundary value problem for the multidimensional elliptic partial differential equation with the Bitsadze-Samarskii-Dirichlet condition. The first and second-orders of accuracy stable difference schemes for the approximate solution of this nonlocal boundary value problem are presented. The stability estimates, coercivity, and almost coercivity inequalities for solution of these schemes are established. The theoretical statements for the solutions of these nonlocal elliptic problems are supported by results of numerical examples.
Nonlinear Preconditioning and its Application in Multicomponent Problems
Liu, Lulu
2015-12-07
The Multiplicative Schwarz Preconditioned Inexact Newton (MSPIN) algorithm is presented as a complement to Additive Schwarz Preconditioned Inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. The ASPIN framework, as an option for the outermost solver, successfully handles strong nonlinearities in computational fluid dynamics, but is barely explored for the highly nonlinear models of complex multiphase flow with capillarity, heterogeneity, and complex geometry. In this dissertation, the fully implicit ASPIN method is demonstrated for a finite volume discretization based on incompressible two-phase reservoir simulators in the presence of capillary forces and gravity. Numerical experiments show that the number of global nonlinear iterations is not only scalable with respect to the number of processors, but also significantly reduced compared with the standard inexact Newton method with a backtracking technique. Moreover, the ASPIN method, in contrast with the IMPES method, saves overall execution time because of the savings in timestep size. We consider the additive and multiplicative types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Moreover, we provide the convergence analysis of the MSPIN algorithm. Under suitable assumptions, it is shown that MSPIN is locally convergent, and desired superlinear or even quadratic convergence can be
Modified Lagrangian and Least Root Approaches for General Nonlinear Optimization Problems
Institute of Scientific and Technical Information of China (English)
W. Oettli; X.Q. Yang
2002-01-01
In this paper we study nonlinear Lagrangian methods for optimization problems with side constraints.Nonlinear Lagrangian dual problems are introduced and their relations with the original problem are established.Moreover, a least root approach is investigated for these optimization problems.
Inverse problem for multi-body interaction of nonlinear waves.
Marruzzo, Alessia; Tyagi, Payal; Antenucci, Fabrizio; Pagnani, Andrea; Leuzzi, Luca
2017-06-14
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we test two methods based on pseudolikelihood, respectively with regularization and with decimation, to determine the coupling constants from sets of measured configurations. We test statistical inference predictions for increasing number of sampled configurations and for an externally tunable temperature-like parameter mimicing real data noise and helping minimization procedures. Analyzed models with phasors and rotors are generalizations of problems of real-valued spherical problems (e.g., density fluctuations), discrete spins (Ising and vectorial Potts) or finite number of states (standard Potts): inference methods presented here can, then, be straightforward applied to a large class of inverse problems. The high versatility of the exposed techniques also concerns the number of expected interactions: results are presented for different graph topologies, ranging from sparse to dense graphs.
Fault detection for nonlinear systems - A standard problem approach
DEFF Research Database (Denmark)
Stoustrup, Jakob; Niemann, Hans Henrik
1998-01-01
The paper describes a general method for designing (nonlinear) fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension...
A Hierarchy of New Nonlinear Evolution Equations Associated with a 3 × 3 Matrix Spectral Problem
Institute of Scientific and Technical Information of China (English)
GENG Xian-Guo; LI Fang
2009-01-01
A 3 × 3 matrix spectral problem with three potentials and the corresponding hierarchy of new nonlinear evolution equations are proposed. Generalized Hamiltonian structures for the hierarchy of nonlinear evolution equations are derived with the aid of trace identity.
Minimization and error estimates for a class of the nonlinear Schrodinger eigenvalue problems
Institute of Scientific and Technical Information of China (English)
MurongJIANG; JiachangSUN
2000-01-01
It is shown that the nonlinear eigenvaiue problem can be transformed into a constrained functional problem. The corresponding minimal function is a weak solution of this nonlinear problem. In this paper, one type of the energy functional for a class of the nonlinear SchrSdinger eigenvalue problems is proposed, the existence of the minimizing solution is proved and the error estimate is given out.
Existence and non-existence results for a nonlinear heat equation
Directory of Open Access Journals (Sweden)
Canan Celik
2007-02-01
Full Text Available In this study, we consider the nonlinear heat equation $$displaylines{ u_{t}(x,t = Delta u(x,t + u(x,t^p quad hbox{in } Omega imes (0,T,cr Bu(x,t = 0 quad hbox{on } partialOmega imes (0,T,cr u(x,0 = u_0(x quad hbox{in } Omega,}$$ with Dirichlet and mixed boundary conditions, where $Omega subset mathbb{R}^n$ is a smooth bounded domain and $p = 1+ 2 /n$ is the critical exponent. For an initial condition $u_0 in L^1$, we prove the non-existence of local solution in $L^1$ for the mixed boundary condition. Our proof is based on comparison principle for Dirichlet and mixed boundary value problems. We also establish the global existence in $L^{1+epsilon}$ to the Dirichlet problem, for any fixed $epsilon > 0$ with $|u_0|_{1+epsilon}$ sufficiently small.
Energy Technology Data Exchange (ETDEWEB)
Zhang, H. [Univ. of Texas, Austin, TX (United States). Dept. of Mathematics
1994-10-01
In this paper the author considers a nonlinear evolution problem denoted in the paper as P. Problem (P) arises in the study of thermal evaporation of atoms and molecules from locally heated surface regions (spikes) invoked as one of several mechanisms of ion-bombardment-induced particle emission (sputtering). Then in the case of particle-induced evaporation, the Stefan-Boltzman law of heat loss by radiation is replaced by some activation law describing the loss of heat by evaporation. The equation in P is the so-called degenerate diffusion problem, which has been extensively studied in recent years. However, when dealing with the nonlinear flux boundary condition, {beta}({center_dot}) is usually assumed to be monotene. The purpose of this paper is to provide a general theory for problem P under a different assumption on {beta}({center_dot}), i.e., Lipschitz continuity instead of monotonicity. The main idea of the proof used here is to choose an appropriate test function from the corresponding linearized dual space of the solution. The similar idea has been used by many authors, e.g., Aronson, Crandall and Peletier, Bertsch and Hilhorst and Friedman. The author follows the proof of Bertsch and Hilhorst. The paper is organized as follows. They begin by stating the precise assumptions on the functions involved in P and by defining a weak solution. Then, in Section 2 they prove the existence of the solution by the method of parabolic regularization. The uniqueness is proved in Section 3. Finally, they study the large time behavior of the solution in Section 4.
Modified Semi-Classical Methods for Nonlinear Quantum Oscillations Problems
Moncrief, Vincent; Maitra, Rachel
2012-01-01
We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical formalism is replaced by an inverted-potential-vanishing-energy variant thereof. Under smoothness, convexity and coercivity hypotheses on its potential energy function, we prove, using the calculus of variations together with the Banach space implicit function theorem, the existence of a global, smooth `fundamental solution'. Higher order quantum corrections, for ground and excited states, are computed through the integration of associated systems of linear transport equations, and formal expansions for the corresponding energy eigenvalues obtained by imposing smoothness on the quantum corrections to the eigenfunctions. For linear oscillators our expansions naturally truncate, reproducing the well-known solutions for the energy eigenfunctions and eigenvalues. As an application, w...
Stability analysis for nonlinear multi－variable delay perturbation problems
Institute of Scientific and Technical Information of China (English)
WangHongshan; ZhangChengjian
2003-01-01
This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems(MVDPP) of the form x′(t) = f(x(t),x(t - τ1(t)),…,x(t -τm(t)),y(t),y(t - τ1(t)),…,y(t - τm(t))), and gy′(t) = g(x(t),x(t- τ1(t)),…,x(t- τm(t)),y(t),y(t- τ1(t)),…,y(t- τm(t))), where 0 < ε <<1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.
THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Mujeeb ur Rehman; Rahmat Ali Khan; Naseer Ahmad Asif
2011-01-01
In this paper,we study existence and uniqueness of solutions to nonlinear three point boundary value problems for fractional differential equation of the type cDδ0+u(t) =f(t,u(t),cDσ0+u(t)),t ∈[0,T],u(0) =αu(η),u(T) =βu(η),where1 ＜δ＜2,0＜σ＜ 1,α,β∈R,η∈(0,T),αη(1-β)+(1-α)(T-βη) ≠0 and cDoδ+,cDσ0+ are the Caputo fractional derivatives.We use Schauder fixed point theorem and contraction mapping principle to obtain existence and uniqueness results.Examples are also included to show the applicability of our results.
On a shock problem involving a nonlinear viscoelastic bar
Directory of Open Access Journals (Sweden)
Tran Ngoc Diem
2005-11-01
Full Text Available We treat an initial boundary value problem for a nonlinear wave equation uttÃ¢ÂˆÂ’uxx+K|u|ÃŽÂ±u+ÃŽÂ»|ut|ÃŽÂ²ut=f(x,t in the domain 0
Approximate Solutions of Delay Parabolic Equations with the Dirichlet Condition
Directory of Open Access Journals (Sweden)
Deniz Agirseven
2012-01-01
Full Text Available Finite difference and homotopy analysis methods are used for the approximate solution of the initial-boundary value problem for the delay parabolic partial differential equation with the Dirichlet condition. The convergence estimates for the solution of first and second orders of difference schemes in Hölder norms are obtained. A procedure of modified Gauss elimination method is used for the solution of these difference schemes. Homotopy analysis method is applied. Comparison of finite difference and homotopy analysis methods is given on the problem.
On the exact controllability of a nonlinear stochastic heat equation
Directory of Open Access Journals (Sweden)
Bui An Ton
2006-01-01
Full Text Available The exact controllability of a nonlinear stochastic heat equation with null Dirichlet boundary conditions, nonzero initial and target values, and an interior control is established.
Some Properties of Complex Matrix-Variate Generalized Dirichlet Integrals
Indian Academy of Sciences (India)
Joy Jacob; Sebastian George; A M Mathai
2005-08-01
Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive definite or hermitian positive definite, are available [4]. Real scalar variables case of the Dirichlet models are generalized in various directions. One such generalization of the type-2 or inverted Dirichlet is looked into in this article. Matrix-variate analogue, when the matrices are hermitian positive definite, are worked out along with some properties which are mathematically and statistically interesting.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, we consider nonlinear infinity-norm minimization problems. We device a reliable Lagrangian dual approach for solving this kind of problems and based on this method we propose an algorithm for the mixed linear and nonlinear infinitynorm minimization problems. Numerical results are presented.
Kalvin, Victor
2011-01-01
We establish a limiting absorption principle for Dirichlet Laplacians in quasi-cylindrical domains. Outside a bounded set these domains can be transformed onto a semi-cylinder by suitable diffeomorphisms. Dirichlet Laplacians model quantum or acoustically-soft waveguides associated with quasi-cylindrical domains. We construct a uniquely solvable problem with perfectly matched layers of finite length. We prove that solutions of the latter problem approximate outgoing or incoming solutions with an error that exponentially tends to zero as the length of layers tends to infinity. Outgoing and incoming solutions are characterized by means of the limiting absorption principle.
Constructing Weyl group multiple Dirichlet series
Chinta, Gautam; Gunnells, Paul E.
2010-01-01
Let Phi be a reduced root system of rank r . A Weyl group multiple Dirichlet series for Phi is a Dirichlet series in r complex variables s_1,dots,s_r , initially converging for {Re}(s_i) sufficiently large, that has meromorphic continuation to {{C}}^r and satisfies functional equations under the transformations of {{C}}^r corresponding to the Weyl group of Phi . A heuristic definition of such a series was given by Brubaker, Bump, Chinta, Friedberg, and Hoffstein, and they have been investigated in certain special cases by others. In this paper we generalize results by Chinta and Gunnells to construct Weyl group multiple Dirichlet series by a uniform method and show in all cases that they have the expected properties.
Text Categorization with Latent Dirichlet Allocation
Directory of Open Access Journals (Sweden)
ZLACKÝ Daniel
2014-05-01
Full Text Available This paper focuses on the text categorization of Slovak text corpora using latent Dirichlet allocation. Our goal is to build text subcorpora that contain similar text documents. We want to use these better organized text subcorpora to build more robust language models that can be used in the area of speech recognition systems. Our previous research in the area of text categorization showed that we can achieve better results with categorized text corpora. In this paper we used latent Dirichlet allocation for text categorization. We divided initial text corpus into 2, 5, 10, 20 or 100 subcorpora with various iterations and save steps. Language models were built on these subcorpora and adapted with linear interpolation to judicial domain. The experiment results showed that text categorization using latent Dirichlet allocation can improve the system for automatic speech recognition by creating the language models from organized text corpora.
ON THE GROWTH OF INFINITE ORDER DIRICHLET SERIES
Institute of Scientific and Technical Information of China (English)
陈特为; 孙道椿
2003-01-01
In this paper, the property of infinite order Dirichlet series in the half-plane areinvestigated. The more exact growth of infinite order Dirichlet series is obtained withoutusing logarithm argument to the type-function for the first time.
Composition Operators on Dirichlet Spaces and Bloch Space
Institute of Scientific and Technical Information of China (English)
Yuan CHENG; Sanjay KUMAR; Ze Hua ZHOU
2014-01-01
In this paper we give a Carleson measure characterization for the compact composition operators between Dirichlet type spaces. We use this characterization to show that every compact composition operator on Dirichlet type spaces is compact on the Bloch space.
Hyperfinite Dirichlet Forms and Stochastic Processes
Albeverio, Sergio; Herzberg, Frederik
2011-01-01
This monograph treats the theory of Dirichlet forms from a comprehensive point of view, using 'nonstandard analysis'. Thus, it is close in spirit to the discrete classical formulation of Dirichlet space theory by Beurling and Deny (1958). The discrete infinitesimal setup makes it possible to study the diffusion and the jump part using essentially the same methods. This setting has the advantage of being independent of special topological properties of the state space and in this sense is a natural one, valid for both finite- and infinite-dimensional spaces. The present monograph provides a tho
Scaling properties of weakly nonlinear coefficients in the Faraday problem.
Skeldon, A C; Porter, J
2011-07-01
Interesting and exotic surface wave patterns have regularly been observed in the Faraday experiment. Although symmetry arguments provide a qualitative explanation for the selection of some of these patterns (e.g., superlattices), quantitative analysis is hindered by mathematical difficulties inherent in a time-dependent, free-boundary Navier-Stokes problem. More tractable low viscosity approximations are available, but these do not necessarily capture the moderate viscosity regime of the most interesting experiments. Here we focus on weakly nonlinear behavior and compare the scaling results derived from symmetry arguments in the low viscosity limit with the computed coefficients of appropriate amplitude equations using both the full Navier-Stokes equations and a reduced set of partial differential equations due to Zhang and Vinãls. We find the range of viscosities over which one can expect "low viscosity" theories to hold. We also find that there is an optimal viscosity range for locating superlattice patterns experimentally-large enough that the region of parameters giving stable patterns is not impracticably small, yet not so large that crucial resonance effects are washed out. These results help explain some of the discrepancies between theory and experiment.
On Nonlinear Approximations to Cosmic Problems with Mixed Boundary Conditions
Mancinelli, P J; Ganon, G; Dekel, A; Mancinelli, Paul J.; Yahil, Amos; Ganon, Galit; Dekel, Avishai
1993-01-01
Nonlinear approximations to problems with mixed boundary conditions are useful for predicting large-scale streaming velocities from the density field, or vice-versa. We evaluate the schemes of Bernardeau \\cite{bernardeau92}, Gramann \\cite{gramann93}, and Nusser \\etal \\cite{nusser91}, using smoothed density and velocity fields obtained from $N$-body simulations of a CDM universe. The approximation of Nusser \\etal is overall the most accurate and robust. For Gaussian smoothing of 1000\\kms\\ the mean error in the approximated relative density perturbation, $\\delta$, is smaller than 0.06, and the dispersion is 0.1. The \\rms\\ error in the estimated velocity is smaller than 60\\kms, and the dispersion is 40\\kms. For smoothing of 500\\kms\\ these numbers increase by about a factor $\\sim 2$ for $\\delta < 4-5$, but deteriorate at higher densities. The other approximations are comparable to those of Nusser \\etal for smoothing of 1000\\kms, but are much less successful for the smaller smoothing of 500\\kms.
Basis properties of eigenfunctions of nonlinear Sturm-Liouville problems
Directory of Open Access Journals (Sweden)
Peter E. Zhidkov
2000-04-01
Full Text Available We consider three nonlinear eigenvalue problems that consist of $$-y''+f(y^2y=lambda y$$ with one of the following boundary conditions: $$displaylines{ y(0=y(1=0 quad y'(0=p ,,cr y'(0=y(1=0 quad y(0=p,, cr y'(0=y'(1=0 quad y(0=p,, }$$ where $p$ is a positive constant. Under smoothness and monotonicity conditions on $f$, we show the existence and uniqueness of a sequence of eigenvalues ${lambda _n}$ and corresponding eigenfunctions ${y_n}$ such that $y_n(x$ has precisely $n$ roots in the interval $(0,1$, where $n=0,1,2,dots$. For the first boundary condition, we show that ${y_n}$ is a basis and that ${y_n/|y_n|}$ is a Riesz basis in the space $L_2(0,1$. For the second and third boundary conditions, we show that ${y_n}$ is a Riesz basis.
Dirichlet and Related Distributions Theory, Methods and Applications
Ng, Kai Wang; Tang, Man-Lai
2011-01-01
The Dirichlet distribution appears in many areas of application, which include modelling of compositional data, Bayesian analysis, statistical genetics, and nonparametric inference. This book provides a comprehensive review of the Dirichlet distribution and two extended versions, the Grouped Dirichlet Distribution (GDD) and the Nested Dirichlet Distribution (NDD), arising from likelihood and Bayesian analysis of incomplete categorical data and survey data with non-response. The theoretical properties and applications are also reviewed in detail for other related distributions, such as the inve
Direct approach for solving nonlinear evolution and two-point boundary value problems
Indian Academy of Sciences (India)
Jonu Lee; Rathinasamy Sakthivel
2013-12-01
Time-delayed nonlinear evolution equations and boundary value problems have a wide range of applications in science and engineering. In this paper, we implement the differential transform method to solve the nonlinear delay differential equation and boundary value problems. Also, we present some numerical examples including time-delayed nonlinear Burgers equation to illustrate the validity and the great potential of the differential transform method. Numerical experiments demonstrate the use and computational efﬁciency of the method. This method can easily be applied to many nonlinear problems and is capable of reducing the size of computational work.
A MESHLESS LOCAL PETROV-GALERKIN METHOD FOR GEOMETRICALLY NONLINEAR PROBLEMS
Institute of Scientific and Technical Information of China (English)
Xiong Yuanbo; Long Shuyao; Hu De'an; Li Guangyao
2005-01-01
Nonlinear formulations of the meshless local Petrov-Galerkin (MLPG) method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficulties in the large deformation analysis. The essential boundary conditions in the present formulation are imposed by a penalty method. An incremental and iterative solution procedure is used to solve geometrically nonlinear problems. Several examples are presented to demonstrate the effectiveness of the method in geometrically nonlinear problems analysis. Numerical results show that the MLPG method is an effective one and that the values of the unknown variable are quite accurate.
Variational Problem with Complex Coefficient of a Nonlinear Schrödinger Equation
Indian Academy of Sciences (India)
Nigar Yildirim Aksoy; Bunyamin Yildiz; Hakan Yetiskin
2012-08-01
An optimal control problem governed by a nonlinear Schrödinger equation with complex coefficient is investigated. The paper studies existence, uniqueness and optimality conditions for the control problem.
Nonlinear predator-prey singularly perturbed Robin Problems for reaction diffusion systems
Institute of Scientific and Technical Information of China (English)
莫嘉琪; 韩祥临
2003-01-01
The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2003-01-01
The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.
THE CAUCHY PROBLEM FOR A CLASS OF DOUBLY DEGENERATE NONLINEAR PARABOLIC EQUATION
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This article studies the Cauchy problem for a class of doubly nonlinear deauthor considers its regularized problem and establishes some estimates. On the basis of the estimates, the existence and uniqueness of the generalized solutions in BV space are proved.
Institute of Scientific and Technical Information of China (English)
LiHongyu; SunJingxian
2005-01-01
By using topological method, we study a class of boundary value problem for a system of nonlinear ordinary differential equations. Under suitable conditions,we prove the existence of positive solution of the problem.
Institute of Scientific and Technical Information of China (English)
SU XIN-WEI
2011-01-01
This paper is devoted to study the existence and uniqueness of solutions to a boundary value problem of nonlinear fractional differential equation with impulsive effects. The arguments are based upon Schauder and Banach fixed-point theorems. We improve and generalize the results presented in [B. Ahmad, S. Sivasundaram, Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations, Nonlinear Analysis: Hybrid Systems, 3(2009), 251258].
A Non-smooth Nonlinear Conjugate Gradient Method for Interactive Contact Force Problems
DEFF Research Database (Denmark)
Silcowitz, Morten; Niebe, Sarah Maria; Erleben, Kenny
2010-01-01
of a nonlinear complementarity problem (NCP), which can be solved using an iterative splitting method, such as the projected Gauss–Seidel (PGS) method. We present a novel method for solving the NCP problem by applying a Fletcher–Reeves type nonlinear nonsmooth conjugate gradient (NNCG) type method. We analyze...
Multisplitting Iteration Schemes for Solving a Class of Nonlinear Complementarity Problems
Institute of Scientific and Technical Information of China (English)
Chen-liang Li; Jin-ping Zeng
2007-01-01
We consider several synchronous and asynchronous multisplitting iteration schemes for solving a class of nonlinear complementarity problems with the system matrix being an H-matrix. We establish the convergence theorems for the schemes. The numerical experiments show that the schemes are efficient for solving the class of nonlinear complementarity problems.
Gharibi, Wajeb
2011-01-01
In this paper, we focus on nonlinear infinite-norm minimization problems that have many applications, especially in computer science and operations research. We set a reliable Lagrangian dual aproach for solving this kind of problems in general, and based on this method, we propose an algorithm for the mixed linear and nonlinear infinite-norm minimization cases with numerical results.
Particle Swarm Optimization-Proximal Point Algorithm for Nonlinear Complementarity Problems
Chai Jun-Feng; Wang Shu-Yan
2013-01-01
A new algorithm is presented for solving the nonlinear complementarity problem by combining the particle swarm and proximal point algorithm, which is called the particle swarm optimization-proximal point algorithm. The algorithm mainly transforms nonlinear complementarity problems into unconstrained optimization problems of smooth functions using the maximum entropy function and then optimizes the problem using the proximal point algorithm as the outer algorithm and particle swarm algorithm a...
Institute of Scientific and Technical Information of China (English)
Zi-you Gao; Tian-de Guo; Guo-ping He; Fang Wu
2002-01-01
In this paper, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints is proposed. Since the new algorithm only needs to solve several systems of linear equations having a same coefficient matrix per iteration, the computation amount of the algorithm is much less than that of the existing SQP algorithms per iteration. Moreover, for the SQPtype algorithms, there exist so-called inconsistent problems, i.e., quadratic programming subproblems of the SQP algorithms may not have a solution at some iterations, but this phenomenon will not occur with the SSLE algorithms because the related systems of linear equations always have solutions. Some numerical results are reported.
Crestel, Benjamin; Alexanderian, Alen; Stadler, Georg; Ghattas, Omar
2017-07-01
The computational cost of solving an inverse problem governed by PDEs, using multiple experiments, increases linearly with the number of experiments. A recently proposed method to decrease this cost uses only a small number of random linear combinations of all experiments for solving the inverse problem. This approach applies to inverse problems where the PDE solution depends linearly on the right-hand side function that models the experiment. As this method is stochastic in essence, the quality of the obtained reconstructions can vary, in particular when only a small number of combinations are used. We develop a Bayesian formulation for the definition and computation of encoding weights that lead to a parameter reconstruction with the least uncertainty. We call these weights A-optimal encoding weights. Our framework applies to inverse problems where the governing PDE is nonlinear with respect to the inversion parameter field. We formulate the problem in infinite dimensions and follow the optimize-then-discretize approach, devoting special attention to the discretization and the choice of numerical methods in order to achieve a computational cost that is independent of the parameter discretization. We elaborate our method for a Helmholtz inverse problem, and derive the adjoint-based expressions for the gradient of the objective function of the optimization problem for finding the A-optimal encoding weights. The proposed method is potentially attractive for real-time monitoring applications, where one can invest the effort to compute optimal weights offline, to later solve an inverse problem repeatedly, over time, at a fraction of the initial cost.
Jiwari, Ram
2015-08-01
In this article, the author proposed two differential quadrature methods to find the approximate solution of one and two dimensional hyperbolic partial differential equations with Dirichlet and Neumann's boundary conditions. The methods are based on Lagrange interpolation and modified cubic B-splines respectively. The proposed methods reduced the hyperbolic problem into a system of second order ordinary differential equations in time variable. Then, the obtained system is changed into a system of first order ordinary differential equations and finally, SSP-RK3 scheme is used to solve the obtained system. The well known hyperbolic equations such as telegraph, Klein-Gordon, sine-Gordon, Dissipative non-linear wave, and Vander Pol type non-linear wave equations are solved to check the accuracy and efficiency of the proposed methods. The numerical results are shown in L∞ , RMS andL2 errors form.
Statistical model of stress corrosion cracking based on extended form of Dirichlet energy
Indian Academy of Sciences (India)
Harry Yosh
2013-12-01
The mechanism of stress corrosion cracking (SCC) has been discussed for decades. Here I propose a model of SCC reflecting the feature of fracture in brittle manner based on the variational principle under approximately supposed thermal equilibrium. In that model the functionals are expressed with extended forms of Dirichlet energy, and Dirichlet principle is applied to them to solve the variational problem that represents SCC and normal extension on pipe surface. Based on the model and the maximum entropy principle, the statistical nature of SCC colony is discussed and it is indicated that the crack has discrete energy and length under ideal isotropy of materials and thermal equilibrium.
R-matrix theory with Dirichlet boundary conditions for integrable electron waveguides
Energy Technology Data Exchange (ETDEWEB)
Lee, Hoshik [Department of Physics, College of William and Mary, Williamsburg, VA 23187 (United States); Reichl, L E, E-mail: hoshik.lee@wm.ed, E-mail: reichl@physics.utexas.ed [Center for Complex Quantum Systems, University of Texas at Austin, Austin, TX 78712 (United States)
2010-10-08
R-matrix theory is used to compute transmission properties of a T-shaped electron waveguide and an electron waveguide-based rotation gate by using Dirichlet boundary conditions for reaction region basis states, even at interfaces with external leads. Such boundary conditions have been known to cause R-matrix convergence problems. We show that an R-matrix obtained using Dirichlet boundary conditions can be convergent for some cases. We also show that R-matrix theory can efficiently reproduce results that were obtained using far more computationally demanding methods such as mode matching techniques, tight-binding Green's function methods or the finite element methods.
A Crank-Nicolson Scheme for the Dirichlet-to-Neumann Semigroup
Directory of Open Access Journals (Sweden)
Rola Ali Ahmad
2015-01-01
Full Text Available The aim of this work is to study a semidiscrete Crank-Nicolson type scheme in order to approximate numerically the Dirichlet-to-Neumann semigroup. We construct an approximating family of operators for the Dirichlet-to-Neumann semigroup, which satisfies the assumptions of Chernoff’s product formula, and consequently the Crank-Nicolson scheme converges to the exact solution. Finally, we write a P1 finite element scheme for the problem, and we illustrate this convergence by means of a FreeFem++ implementation.
A multiplicity result for a class of quasilinear elliptic and parabolic problems
Directory of Open Access Journals (Sweden)
M. R. Grossinho
1997-04-01
Full Text Available We prove the existence of infinitely many solutions for a class of quasilinear elliptic and parabolic equations, subject respectively to Dirichlet and Dirichlet-periodic boundary conditions. We assume that the primitive of the nonlinearity at the right-hand side oscillates at infinity. The proof is based on the construction of upper and lower solutions, which are obtained as solutions of suitable comparison equations. This method allows the introduction of conditions on the potential for the study of parabolic problems, as well as to treat simultaneously the singular and the degenerate case.
Vargas-Magaña, Rosa; Panayotaros, Panayotis
2015-11-01
We study the problem of wave propagation in a long-wave asymptotic regime over variable bottom of an ideal irrotational fluid in the framework of the Hamiltonian formulation in which the non-local Dirichlet-Neumann (DtN) operator appears explicitly in the Hamiltonian. We propose a non-local Hamiltonian model for bidirectional wave propagation in shallow water that involves pseudodifferential operators that approximate the DtN operator for variable depth. These models generalize the Boussinesq system as they include the exact dispersion relation in the case of constant depth. We present results for the normal modes and eigenfrequencies of the linearized problem. We see that variable topography introduces effects such as steepening of normal modes with increasing variation of depth, as well as amplitude modulation of the normal modes in certain wavelength ranges. Numerical integration shows that the constant depth nonlocal Boussinesq model with quadratic nonlinearity can capture the evolution obtained with higher order approximations of the DtN operator. In the case of variable depth we observe certain oscillations in width of the crest and also some interesting textures in the evolution of wave crests during the passage from obstacles.
Dual variational formulas for the first Dirichlet eigenvalue on half-line
Institute of Scientific and Technical Information of China (English)
Chen; Mufa(陈木法); ZHANG; Yuhui(张余辉); ZHAO; Xiaoliang(赵晓亮)
2003-01-01
The aim of the paper is to establish two dual variational formulas for the first Dirichlet eigenvalue of the second order elliptic operators on half-line. Some explicit bounds of the eigenvalue depending only on the coefficients of the operators are presented. Moreover, the corresponding problems in the discrete case and the higher-order eigenvalues in the continuous case are also studied.
Costiner, Sorin; Taasan, Shlomo
1994-01-01
This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.
Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case
Directory of Open Access Journals (Sweden)
Georg S. Weiss
2004-03-01
Full Text Available We derive a monotonicity formula at boundary points for a class of nonlinear elliptic partial differential equations, including the obstacle problem case, quenching, a free boundary problem with Bernoulli-type free boundary condition as well as the blow-up case. As application model we prove - for Dirichlet boundary data satisfying certain assumptions - the global existence of a classical solution of the free boundary problem with Bernoulli-type free boundary condition in two and three dimensions.
Lossless Convexification of Control Constraints for a Class of Nonlinear Optimal Control Problems
Blackmore, Lars; Acikmese, Behcet; Carson, John M.,III
2012-01-01
In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field.
Freeform illumination design: a nonlinear boundary problem for the elliptic Monge-Ampére equation.
Wu, Rengmao; Xu, Liang; Liu, Peng; Zhang, Yaqin; Zheng, Zhenrong; Li, Haifeng; Liu, Xu
2013-01-15
We propose an approach to deal with the problem of freeform surface illumination design without assuming any symmetry based on the concept that this problem is similar to the problem of optimal mass transport. With this approach, the freeform design is converted into a nonlinear boundary problem for the elliptic Monge-Ampére equation. The theory and numerical method are given for solving this boundary problem. Experimental results show the feasibility of this approach in tackling this freeform design problem.
Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems
Cerro, J. A.; Scotti, S. J.
1991-01-01
Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.
Peng, Haijun; Wang, Xinwei; Zhang, Sheng; Chen, Biaosong
2017-07-01
Nonlinear state-delayed optimal control problems have complex nonlinear characters. To solve this complex nonlinear problem, an iterative symplectic pseudospectral method based on quasilinearization techniques, the dual variational principle and pseudospectral methods is proposed in this paper. First, the proposed method transforms the original nonlinear optimal control problem into a series of linear quadratic optimal control problems. Then, a symplectic pseudospectral method is developed to solve these converted linear quadratic state-delayed optimal control problems. Coefficient matrices in the proposed method are sparse and symmetric since the dual variational principle is used, which makes the proposed method highly efficient. Converged numerical solutions with high precision can be obtained after a few iterations due to the benefit of the local pseudospectral method and quasilinearization techniques. In the numerical simulations, other numerical methods were used for comparisons. The numerical simulation results show that the proposed method is highly accurate, efficient and robust.
Energy Technology Data Exchange (ETDEWEB)
Zou, Li [Dalian Univ. of Technology, Dalian City (China). State Key Lab. of Structural Analysis for Industrial Equipment; Liang, Songxin; Li, Yawei [Dalian Univ. of Technology, Dalian City (China). School of Mathematical Sciences; Jeffrey, David J. [Univ. of Western Ontario, London (Canada). Dept. of Applied Mathematics
2017-06-01
Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.
Zou, Li; Liang, Songxin; Li, Yawei; Jeffrey, David J.
2017-03-01
Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.
Control design for the nonlinear benchmark problem via the output regulation method
Institute of Scientific and Technical Information of China (English)
Jie HUANG; Guoqiang HU
2004-01-01
The problem of designing a feedback controller to achieve asymptotic disturbance rejection / attenuation while maintaining good transient response in the RTAC system is known as a benchmark nonlinear control problem, which has been an intensive research subject since 1995. In this paper, we will further investigate the solvability of the robust disturbance rejection problem of the RTAC system by the measurement output feedback control based on the robust output regulation method. We have obtained a design by overcoming two major obstacles: find a closed-form solution of the regulator equations; and devise a nonlinear internal model to account for non-polynomial nonlinearities.
Solving Large Scale Nonlinear Eigenvalue Problem in Next-Generation Accelerator Design
Energy Technology Data Exchange (ETDEWEB)
Liao, Ben-Shan; Bai, Zhaojun; /UC, Davis; Lee, Lie-Quan; Ko, Kwok; /SLAC
2006-09-28
A number of numerical methods, including inverse iteration, method of successive linear problem and nonlinear Arnoldi algorithm, are studied in this paper to solve a large scale nonlinear eigenvalue problem arising from finite element analysis of resonant frequencies and external Q{sub e} values of a waveguide loaded cavity in the next-generation accelerator design. They present a nonlinear Rayleigh-Ritz iterative projection algorithm, NRRIT in short and demonstrate that it is the most promising approach for a model scale cavity design. The NRRIT algorithm is an extension of the nonlinear Arnoldi algorithm due to Voss. Computational challenges of solving such a nonlinear eigenvalue problem for a full scale cavity design are outlined.
Initial-boundary value problems for a class of nonlinear thermoelastic plate equations
Institute of Scientific and Technical Information of China (English)
Zhang Jian-Wen; Rong Xiao-Liang; Wu Run-Heng
2009-01-01
This paper studies initial-boundary value problems for a class of nonlinear thermoelastic plate equations. Under some certain initial data and boundary conditions,it obtains an existence and uniqueness theorem of global weak solutions of the nonlinear thermoelstic plate equations,by means of the Galerkin method. Moreover,it also proves the existence of strong and classical solutions.
Analytical Solution of Nonlinear Problems in Classical Dynamics by Means of Lagrange-Ham
DEFF Research Database (Denmark)
Kimiaeifar, Amin; Mahdavi, S. H; Rabbani, A.
2011-01-01
In this work, a powerful analytical method, called Homotopy Analysis Methods (HAM) is coupled with Lagrange method to obtain the exact solution for nonlinear problems in classic dynamics. In this work, the governing equations are obtained by using Lagrange method, and then the nonlinear governing...
NONLOCAL INITIAL PROBLEM FOR NONLINEAR NONAUTONOMOUS DIFFERENTIAL EQUATIONS IN A BANACH SPACE
Institute of Scientific and Technical Information of China (English)
M.I.Gil＇
2004-01-01
The nonlocal initial problem for nonlinear nonautonomous evolution equations in a Banach space is considered. It is assumed that the nonlinearities have the local Lipschitz properties. The existence and uniqueness of mild solutions are proved. Applications to integro-differential equations are discussed. The main tool in the paper is the normalizing mapping (the generalized norm).
Cognitive Variables in Problem Solving: A Nonlinear Approach
Stamovlasis, Dimitrios; Tsaparlis, Georgios
2005-01-01
We employ tools of complexity theory to examine the effect of cognitive variables, such as working-memory capacity, degree of field dependence-independence, developmental level and the mobility-fixity dimension. The nonlinear method correlates the subjects' rank-order achievement scores with each cognitive variable. From the achievement scores in…
CLASSIFICATION OF BIFURCATIONS FOR NONLINEAR DYNAMICAL PROBLEMS WITH CONSTRAINTS
Institute of Scientific and Technical Information of China (English)
吴志强; 陈予恕
2002-01-01
Bifurcation of periodic solutions widely existed in nonlinear dynamical systems isa kind of constrained one in intrinsic quality because its amplitude is always non-negative.Classification of the bifurcations with the type of constraint was discussed. All its six typesof transition sets are derived, in which three types are newly found and a method isproposed for analyzing the constrained bifurcation.
Nonlocal Cauchy problem for nonlinear mixed integrodifferential equations
Directory of Open Access Journals (Sweden)
H.L. Tidke
2010-12-01
Full Text Available The present paper investigates the existence and uniqueness of mild and strong solutions of a nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition. The results obtained by using Schauder fixed point theorem and the theory of semigroups.
Novel Reduced Order in Time Models for Problems in Nonlinear Aeroelasticity Project
National Aeronautics and Space Administration — Research is proposed for the development and implementation of state of the art, reduced order models for problems in nonlinear aeroelasticity. Highly efficient and...
The Expansion of Dynamic Solving Process About a Class of Non-linear Programming Problems
Institute of Scientific and Technical Information of China (English)
ZANG Zhen-chun
2001-01-01
In this paper, we research non-linear programming problems which have a given specialstructure, some simple forms of this kind structure have been solved in some papers, here we focus on othercomplex ones.
LEAST-SQUARES MIXED FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS
Institute of Scientific and Technical Information of China (English)
Dan-ping Yang
2002-01-01
Two least-squares mixed finite element schemes are formulated to solve the initialboundary value problem of a nonlinear parabolic partial differential equation and the convergence of these schemes are analyzed.
Institute of Scientific and Technical Information of China (English)
张建军; 王德人
2004-01-01
In this paper, based on the resuls presented in part I of this paper[18],we present a numerical crabeding algorithm for soling the nonlinear complementarity problem, and prove its convergence carefully. Numerical experiments show that the algorithm is successful.
SIMILARITY REDUCTIONS FOR THE NONLINEAR EVOLUTION EQUATION ARISING IN THE FERMI-PASTA-ULAM PROBLEM
Institute of Scientific and Technical Information of China (English)
谢福鼎; 闫振亚; 张鸿庆
2002-01-01
Four families of similarity reductions are obtained for the nonlinear evolution equation arising in the Fermi-Pasta-Ulam problem via using both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou.
Hybrid bounds for Dirichlet's L-function
Huxley, M. N.; Watt, N.
2000-11-01
This is a paper about upper bounds for Dirichlet's L-function, L(s, [chi]), on its critical line (s + s¯ = 1). It is to be assumed throughout that, unless otherwise stated, the Dirichlet character, [chi], is periodic modulo a prime, r, and is not the principal character mod r. Our main theorem below shows that, if [epsilon] > 0, thenformula here(where A is an absolute constant), for 0 < [alpha] = (log r)/(log t) [less-than-or-eq, slant] 2/753 [minus sign] [epsilon]. Somewhat weaker bounds are obtained for other cases where 0 < [alpha] [less-than-or-eq, slant] 11/180 [minus sign] [epsilon]. Note that in [13] it was shown that, for 0 < [alpha] [less-than-or-eq, slant] 2/57,formula hereOur main theorem is a corollary of the new bounds we prove for certain exponential sums, S, with a Dirichlet character factor:formula herewhere M2 [less-than-or-eq, slant] 2M and f(x) is a real function whose derivatives satisfy certain conditions restricting their size.
Perpetuity property of the Dirichlet distribution
Hitczenko, Pawel
2012-01-01
Let $X$, $B$ and $Y$ be three Dirichlet, Bernoulli and beta independent random variables such that $X\\sim \\mathcal{D}(a_0,...,a_d),$ such that $\\Pr(B=(0,...,0,1,0,...,0))=a_i/a$ with $a=\\sum_{i=0}^da_i$ and such that $Y\\sim \\beta(1,a).$ We prove that $X\\sim X(1-Y)+BY.$ This gives the stationary distribution of a simple Markov chain on a tetrahedron. We also extend this result to the case when $B$ follows a quasi Bernoulli distribution $\\mathcal{B}_k(a_0,...,a_d)$ on the tetrahedron and when $Y\\sim \\beta(k,a)$. We extend it even more generally to the case where $X$ is a Dirichlet process and $B$ is a quasi Bernoulli random probability. Finally the case where the integer $k$ is replaced by a positive number $c$ is considered when $a_0=...=a_d=1.$ \\textsc{Keywords} \\textit{Perpetuities, Dirichlet process, Ewens distribution, quasi Bernoulli laws, probabilities on a tetrahedron, $T_c$ transform, stationary distribution.} AMS classification 60J05, 60E99.
Existence Theorems for Nonlinear Boundary Value Problems for Second Order Differential Inclusions
Kandilakis, Dimitrios A.; Papageorgiou, Nikolaos S.
1996-11-01
In this paper we consider a nonlinear two-point boundary value problem for second order differential inclusions. Using the Leray-Schauder principle and its multivalued analog due to Dugundji-Granas, we prove existence theorems for convex and nonconvex problems. Our results are quite general and incorporate as special cases several classes of problems which are of interest in the literature.
A NUMERICAL EMBEDDING METHOD FOR SOLVING THE NONLINEAR COMPLEMENTARITY PROBLEM(Ⅰ)--THEORY
Institute of Scientific and Technical Information of China (English)
Jian-jun Zhang; De-ren Wang
2002-01-01
In this paper, we extend the numerical embedding method for solving the smooth equations to the nonlinear complementarity problem. By using the nonsmooth theory,we prove the existence and the continuation of the following path for the corresponding homotopy equations. Therefore the basic theory of the numerical embedding method for solving the nonlinear complementarity problem is established. In part Ⅱ of this paper, we will further study the implementation of the method and give some numerical exapmles.
Discussion of Some Problems About Nonlinear Time Series Prediction Using v-Support Vector Machine
Institute of Scientific and Technical Information of China (English)
GAO Cheng-Feng; CHEN Tian-Lun; NAN Tian-Shi
2007-01-01
Some problems in using v-support vector machine (v-SVM) for the prediction of nonlinear time series are discussed. The problems include selection of various net parameters, which affect the performance of prediction, mixture of kernels, and decomposition cooperation linear programming v-SVM regression, which result in improvements of the algorithm. Computer simulations in the prediction of nonlinear time series produced by Mackey-Glass equation and Lorenz equation provide some improved results.
Optimality Condition and Wolfe Duality for Invex Interval-Valued Nonlinear Programming Problems
Directory of Open Access Journals (Sweden)
Jianke Zhang
2013-01-01
Full Text Available The concepts of preinvex and invex are extended to the interval-valued functions. Under the assumption of invexity, the Karush-Kuhn-Tucker optimality sufficient and necessary conditions for interval-valued nonlinear programming problems are derived. Based on the concepts of having no duality gap in weak and strong sense, the Wolfe duality theorems for the invex interval-valued nonlinear programming problems are proposed in this paper.
Efficient Realization of the Mixed Finite Element Discretization for nonlinear Problems
Knabner, Peter; Summ, Gerhard
2016-01-01
We consider implementational aspects of the mixed finite element method for a special class of nonlinear problems. We establish the equivalence of the hybridized formulation of the mixed finite element method to a nonconforming finite element method with augmented Crouzeix-Raviart ansatz space. We discuss the reduction of unknowns by static condensation and propose Newton's method for the solution of local and global systems. Finally, we show, how such a nonlinear problem arises from the mixe...
Zhang, Songchuan; Xia, Youshen
2016-12-28
Much research has been devoted to complex-variable optimization problems due to their engineering applications. However, the complex-valued optimization method for solving complex-variable optimization problems is still an active research area. This paper proposes two efficient complex-valued optimization methods for solving constrained nonlinear optimization problems of real functions in complex variables, respectively. One solves the complex-valued nonlinear programming problem with linear equality constraints. Another solves the complex-valued nonlinear programming problem with both linear equality constraints and an ℓ₁-norm constraint. Theoretically, we prove the global convergence of the proposed two complex-valued optimization algorithms under mild conditions. The proposed two algorithms can solve the complex-valued optimization problem completely in the complex domain and significantly extend existing complex-valued optimization algorithms. Numerical results further show that the proposed two algorithms have a faster speed than several conventional real-valued optimization algorithms.
Nonlinear problems of complex natural systems: Sun and climate dynamics.
Bershadskii, A
2013-01-13
The universal role of the nonlinear one-third subharmonic resonance mechanism in generation of strong fluctuations in complex natural dynamical systems related to global climate is discussed using wavelet regression detrended data. The role of the oceanic Rossby waves in the year-scale global temperature fluctuations and the nonlinear resonance contribution to the El Niño phenomenon have been discussed in detail. The large fluctuations in the reconstructed temperature on millennial time scales (Antarctic ice core data for the past 400,000 years) are also shown to be dominated by the one-third subharmonic resonance, presumably related to the Earth's precession effect on the energy that the intertropical regions receive from the Sun. The effects of galactic turbulence on the temperature fluctuations are also discussed.
Some Problems in Nonlinear Dynamic Instability and Bifurcation Theory for Engineering Structures
Institute of Scientific and Technical Information of China (English)
彭妙娟; 程玉民
2005-01-01
In civil engineering, the nonlinear dynamic instability of structures occurs at a bifurcation point or a limit point. The instability at a bifurcation point can be analyzed with the theory of nonlinear dynamics, and that at a limit point can be discussed with the theory of elastoplasticity. In this paper, the nonlinear dynamic instability of structures was treated with mathematical and mechanical theories. The research methods for the problems of structural nonlinear dynamic stability were discussed first, and then the criterion of stability or instability of structures, the method to obtain the bifurcation point and the limit point, and the formulae of the directions of the branch solutions at a bifurcation point were elucidated. These methods can be applied to the problems of nonlinear dynamic instability of structures such as reticulated shells, space grid structures, and so on.
Lie and Conditional Symmetries of a Class of Nonlinear (1 + 2-Dimensional Boundary Value Problems
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Roman Cherniha
2015-08-01
Full Text Available A new definition of conditional invariance for boundary value problems involving a wide range of boundary conditions (including initial value problems as a special case is proposed. It is shown that other definitions worked out in order to find Lie symmetries of boundary value problems with standard boundary conditions, followed as particular cases from our definition. Simple examples of direct applicability to the nonlinear problems arising in applications are demonstrated. Moreover, the successful application of the definition for the Lie and conditional symmetry classification of a class of (1 + 2-dimensional nonlinear boundary value problems governed by the nonlinear diffusion equation in a semi-infinite domain is realised. In particular, it is proven that there is a special exponent, k ≠ —2, for the power diffusivity uk when the problem in question with non-vanishing flux on the boundary admits additional Lie symmetry operators compared to the case k ≠ —2. In order to demonstrate the applicability of the symmetries derived, they are used for reducing the nonlinear problems with power diffusivity uk and a constant non-zero flux on the boundary (such problems are common in applications and describing a wide range of phenomena to (1 + 1-dimensional problems. The structure and properties of the problems obtained are briefly analysed. Finally, some results demonstrating how Lie invariance of the boundary value problem in question depends on the geometry of the domain are presented.
A NUMERICAL CALCULATION METHOD FOR EIGENVALUE PROBLEMS OF NONLINEAR INTERNAL WAVES
Institute of Scientific and Technical Information of China (English)
SHI Xin-gang; FAN Zhi-song; LIU Hai-long
2009-01-01
Generally speaking, the background shear current U(z)must be taken into account in eigenvalue problems of nonlinear internal waves in ocean, as is different from those of linear internal waves. A numerical calculation method for eigenvalue problems of nonlinear internal waves is presented in this paper on the basis of the Thompson-Haskell's calculation method. As an application of this method, at a station (21°N, 117°15′E) in the South China Sea, a modal structure and parameters of nonlinear internal waves are calculated, and the results closely agree with the calculated results based on observation by Yang et al..
Wang, Qing; Yao, Jing-Zheng
2010-12-01
Several algorithms were proposed relating to the development of a framework of the perturbation-based stochastic finite element method (PSFEM) for large variation nonlinear dynamic problems. For this purpose, algorithms and a framework related to SFEM based on the stochastic virtual work principle were studied. To prove the validity and practicality of the algorithms and framework, numerical examples for nonlinear dynamic problems with large variations were calculated and compared with the Monte-Carlo Simulation method. This comparison shows that the proposed approaches are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.
Institute of Scientific and Technical Information of China (English)
Igor Boglaev; Matthew Hardy
2008-01-01
This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type.To solve the nonlinear weighted average finite difference scheme for the partial differential equation,we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition.This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. The rate of convergence of the monotone domain decomposition algorithm is estimated.Numerical experiments are presented.
DEFF Research Database (Denmark)
Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari
2010-01-01
Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...... and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However...
Well-posedness for a generalized derivative nonlinear Schrödinger equation
Hayashi, Masayuki; Ozawa, Tohru
2016-11-01
We study the Cauchy problem for a generalized derivative nonlinear Schrödinger equation with the Dirichlet boundary condition. We establish the local well-posedness results in the Sobolev spaces H1 and H2. Solutions are constructed as a limit of approximate solutions by a method independent of a compactness argument. We also discuss the global existence of solutions in the energy space H1.
Nonlinear elliptic equations of the second order
Han, Qing
2016-01-01
Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler-Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and "elementary" proofs for results in important special cases. This book will serve as a valuable resource for graduate stu...
Institute of Scientific and Technical Information of China (English)
高永馨
2002-01-01
Studies the existence of solutions of nonlinear two point boundary value problems for nonlinear 4n-th-order differential equation y(4n)= f( t,y,y' ,y",… ,y(4n－1) ) (a) with the boundary conditions g2i(y(2i) (a) ,y(2i+1) (a)) = 0,h2i(y(2i) (c) ,y(2i+1) (c)) = 0, (I= 0,1,…,2n － 1 ) (b) where the functions f, gi and hi are continuous with certain monotone properties. For the boundary value problems of nonlinear nth order differential equation y(n) = f(t,y,y',y",… ,y(n－1)) many results have been given at the present time. But the existence of solutions of boundary value problem (a), (b) studied in this paper has not been covered by the above researches. Moreover, the corollary of the important theorem in this paper, I.e. Existence of solutions of the boundary value problem. Y(4n) = f(t,y,y',y",… ,y(4n－1) ) a2iy(2i) (at) + a2i+1y(2i+1) (a) = b2i ,c2iy(2O ( c ) + c2i+1y(2i+1) ( c ) = d2i, ( I = 0,1 ,…2n － 1) has not been dealt with in previous works.
2016-01-01
A review of studies performed using the R-functions theory to solve problems of nonlinear dynamics of plates and shallow shells is presented. The systematization of results and studies for the problems of free and parametric vibrations and for problems of static and dynamic stability is fulfilled. Expansion of the developed original method of discretization for nonlinear movement equations on new classes of nonlinear problems is shown. These problems include researches of vibratio...
Enokida, Ryuta; Takewaki, Izuru; Stoten, David
2014-12-01
The problem of control system design can be conceptualised as identifying an input signal to a plant (the system to be controlled) so that the corresponding output matches that of a pre-defined reference signal. Primarily, this problem is solved via well-known techniques based upon the principle of feedback design, an essential component for ensuring stability and robustness of the controlled system. However, feedforward design techniques also have a large part to play, whereby (in the absence of feedback control and assuming that the plant is stable) a model of the plant dynamics can be used to modify the reference signal so that the resultant feedforward input signal generates a plant output signal that is sufficiently close to the original reference signal. The principal objective of this paper is to introduce a new nonlinear control method, called nonlinear signal-based control (NSBC) that can be executed as an on-line technique of feedforward compensation (used synonymously here with the phrase 'input identification') and an off-line technique of feedback compensation. NSBC determines the feedforward input signal to the plant by using an error signal, determined from the difference between the output signals from a linear model of the plant and from the nonlinear plant, under the same input signal. The efficacy of NSBC is examined via numerical examples using Matlab/Simulink and compared with alternative well-known methods based upon inverse transfer function compensation and also the method of high gain feedback control. NSBC was found to provide the most accurate input identification in all the examined cases of linear or nonlinear single-input, single-output and single-input, multi-output (SIMO) systems. Furthermore, in problems of structural and earthquake engineering, NSBC was also found to be particularly effective in estimating the original ground motion from a nonlinear SIMO system and its response.
Cotta, R. M.; Naveira-Cotta, C. P.; Knupp, D. C.; Zotin, J. L. Z.; Pontes, P. C.
2016-09-01
This lecture offers an updated review on the Generalized Integral Transform Technique (GITT), with focus on handling complex geometries, coupled problems, and nonlinear convection-diffusion, so as to illustrate some new application paradigms. Special emphasis is given to demonstrating novel developments, such as a single domain reformulation strategy that simplifies the treatment of complex geometries, an integral balance scheme in handling multiscale problems, the adoption of convective eigenvalue problems in dealing with strongly convective formulations, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Representative application examples are then provided that employ recent extensions on the Generalized Integral Transform Technique (GITT), and a few numerical results are reported to illustrate the convergence characteristics of the proposed eigenfunction expansions.
DOUBLE TRIALS METHOD FOR NONLINEAR PROBLEMS ARISING IN HEAT TRANSFER
Directory of Open Access Journals (Sweden)
Chun-Hui He
2011-01-01
Full Text Available According to an ancient Chinese algorithm, the Ying Buzu Shu, in about second century BC, known as the rule of double false position in West after 1202 AD, two trial roots are assumed to solve algebraic equations. The solution procedure can be extended to solve nonlinear differential equations by constructing an approximate solution with an unknown parameter, and the unknown parameter can be easily determined using the Ying Buzu Shu. An example in heat transfer is given to elucidate the solution procedure.
Method of guiding functions in problems of nonlinear analysis
Obukhovskii, Valeri; Van Loi, Nguyen; Kornev, Sergei
2013-01-01
This book offers a self-contained introduction to the theory of guiding functions methods, which can be used to study the existence of periodic solutions and their bifurcations in ordinary differential equations, differential inclusions and in control theory. It starts with the basic concepts of nonlinear and multivalued analysis, describes the classical aspects of the method of guiding functions, and then presents recent findings only available in the research literature. It describes essential applications in control theory, the theory of bifurcations, and physics, making it a valuable resource not only for “pure” mathematicians, but also for students and researchers working in applied mathematics, the engineering sciences and physics.
Dynamics of parabolic problems with memory. Subcritical and critical nonlinearities
Li, Xiaojun
2016-08-01
In this paper, we study the long-time behavior of the solutions of non-autonomous parabolic equations with memory in cases when the nonlinear term satisfies subcritical and critical growth conditions. In order to do this, we show that the family of processes associated to original systems with heat source f(x, t) being translation bounded in Lloc 2 ( R ; L 2 ( Ω ) ) is dissipative in higher energy space M α , 0 < α ≤ 1, and possesses a compact uniform attractor in M 0 .
Li, Dongfang; Zhang, Jiwei
2016-10-01
Anomalous diffusion behavior in many practical problems can be described by the nonlinear time-fractional parabolic problems on unbounded domain. The numerical simulation is a challenging problem due to the dependence of global information from time fractional operators, the nonlinearity of the problem and the unboundedness of the spacial domain. To overcome the unboundedness, conventional computational methods lead to extremely expensive costs, especially in high dimensions with a simple treatment of boundary conditions by making the computational domain large enough. In this paper, based on unified approach proposed in [25], we derive the efficient nonlinear absorbing boundary conditions (ABCs), which reformulates the problem on unbounded domain to an initial boundary value problem on bounded domain. To overcome nonlinearity, we construct a linearized finite difference scheme to solve the reduced nonlinear problem such that iterative methods become dispensable. And the stability and convergence of our linearized scheme are proved. Most important, we prove that the numerical solutions are bounded by the initial values with a constant coefficient, i.e., the constant coefficient is independent of the time. Overall, the computational cost can be significantly reduced comparing with the usual implicit schemes and a simple treatment of boundary conditions. Finally, numerical examples are given to demonstrate the efficiency of the artificial boundary conditions and theoretical results of the schemes.
A NUMERICAL METHOD FOR NONLINEAR WATER WAVES
Institute of Scientific and Technical Information of China (English)
ZHAO Xi-zeng; SUN Zhao-chen; LIANG Shu-xiu; HU Chang-hong
2009-01-01
This article presents a numerical method for modeling nonlinear water waves based on the High Order Spectral (HOS) method proposed by Dommermuth and Yue and West et al., involving Taylor expansion of the Dirichlet problem and the Fast Fourier Transform (FFT) algorithm. The validation and efficiency of the numerical scheme is illustrated by a number of case studies on wave and wave train configuration including the evolution of fifth-order Stokes waves, wave dispersive focusing and the instability of Stokes wave with finite slope. The results agree well with those obtained by other studies.
Nonlinear boundary value problem for biregular functions in Clifford analysis
Institute of Scientific and Technical Information of China (English)
黄沙
1996-01-01
The biregular function in Clifford analysis is discussed. Plemelj’s formula is obtained andnonlinear boundary value problem: is considered. Applying the methodof integral equations and Schauder fixed-point theorem, the existence of solution for the above problem is proved.
A Class of Dynamic Nonlinear Resource Allocation Problems
1989-10-01
algorithm and presents some numerical results in [5]. Matlin [6] provides a review of the literature on weapon-target allocation problems. Several...weapon, multi-target assignment problem," Working Paper 26957, MITRE, Feb. 1986. [6] S. M. Matlin , "A review of the literature on the missile
Nonlinear problems of complex natural systems: Sun and climate dynamics
Bershadskii, A
2012-01-01
Universal role of the nonlinear one-third subharmonic resonance mechanism in generation of the strong fluctuations in such complex natural dynamical systems as global climate and global solar activity is discussed using wavelet regression detrended data. Role of the oceanic Rossby waves in the year-scale global temperature fluctuations and the nonlinear resonance contribution to the El Nino phenomenon have been discussed in detail. The large fluctuations of the reconstructed temperature on the millennial time-scales (Antarctic ice cores data for the past 400,000 years) are also shown to be dominated by the one-third subharmonic resonance, presumably related to Earth precession effect on the energy that the intertropical regions receive from the Sun. Effects of Galactic turbulence on the temperature fluctuations are discussed in this content. It is also shown that the one-third subharmonic resonance can be considered as a background for the 11-years solar cycle, and again the global (solar) rotation and chaoti...
Institute of Scientific and Technical Information of China (English)
Li WANG; Jixiu WANG
2014-01-01
Let B1 ⊂ RN be a unit ball centered at the origin. The main purpose of this paper is to discuss the critical dimension phenomenon for radial solutions of the following quasilinear elliptic problem involving critical Sobolev exponent and singular coefficients:-div(|∇u|p-2∇u)=|x|s|u|p*(s)-2u+λ|x|t|u|p-2u, x∈B1, u|∂B1 =0, where t, s>-p, 2≤pp(p-1)t+p(p2-p+1) andλ∈(0,λ1,t), whereλ1,t is the first eigenvalue of-∆p with the Dirichlet boundary condition. Meanwhile, the nonexistence of sign-changing radial solutions is proved if the space dimension N ≤ (ps+p) min{1, p+tp+s}+p2p-(p-1) min{1, p+tp+s} andλ>0 is small.
The Hierarchical Dirichlet Process Hidden Semi-Markov Model
Johnson, Matthew J
2012-01-01
There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the traditional HMM. However, in many settings the HDP-HMM's strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can extend the HDP-HMM to capture such structure by drawing upon explicit-duration semi- Markovianity, which has been developed in the parametric setting to allow construction of highly interpretable models that admit natural prior information on state durations. In this paper we introduce the explicitduration HDP-HSMM and develop posterior sampling algorithms for efficient inference in both the direct-assignment and weak-limit approximation settings. We demonstrate the utility of the model and our inference methods on synthetic data as well as experiments on a speaker diarization problem and an example of learning the patterns in Morse code.
Background Subtraction with DirichletProcess Mixture Models.
Haines, Tom S F; Tao Xiang
2014-04-01
Video analysis often begins with background subtraction. This problem is often approached in two steps-a background model followed by a regularisation scheme. A model of the background allows it to be distinguished on a per-pixel basis from the foreground, whilst the regularisation combines information from adjacent pixels. We present a new method based on Dirichlet process Gaussian mixture models, which are used to estimate per-pixel background distributions. It is followed by probabilistic regularisation. Using a non-parametric Bayesian method allows per-pixel mode counts to be automatically inferred, avoiding over-/under- fitting. We also develop novel model learning algorithms for continuous update of the model in a principled fashion as the scene changes. These key advantages enable us to outperform the state-of-the-art alternatives on four benchmarks.
Multiple optimal solutions to a sort of nonlinear optimization problem
Institute of Scientific and Technical Information of China (English)
Xue Shengjia
2007-01-01
The optimization problem is considered in which the objective function is pseudolinear(both pseudoconvex and pseudoconcave) and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions ( ifthe uniqueness condition is not satisfied ) are provided. Finally, an illustrative example is also given.
Nonlinear Multidimensional Assignment Problems Efficient Conic Optimization Methods and Applications
2015-06-24
CONTRACT NUMBER 5b. GRANT NUMBER FA9550-12-1-0153 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Mittelmann, Hans D 5d. PROJECT NUMBER 5e. TASK NUMBER 5f...problems. The size 16 three-dimensional quadratic assignment problem Q3AP from wireless communications was solved using a sophisticated approach...placement of the sensors. However, available MINLP solvers are not sufficiently effective, even in the convex case, and a hybrid Benders
Directory of Open Access Journals (Sweden)
Mahdi Sohrabi-Haghighat
2014-06-01
Full Text Available In this paper, a new algorithm based on SQP method is presented to solve the nonlinear inequality constrained optimization problem. As compared with the other existing SQP methods, per single iteration, the basic feasible descent direction is computed by solving at most two equality constrained quadratic programming. Furthermore, there is no need for any auxiliary problem to obtain the coefficients and update the parameters. Under some suitable conditions, the global and superlinear convergence are shown. Keywords: Global convergence, Inequality constrained optimization, Nonlinear programming problem, SQP method, Superlinear convergence rate.
CONVERGENCE OF THE CRANK-NICOLSON/NEWTON SCHEME FOR NONLINEAR PARABOLIC PROBLEM
Institute of Scientific and Technical Information of China (English)
Xinlong FENG; Yinnian HE
2016-01-01
In this paper, the Crank-Nicolson/Newton scheme for solving numerically second-order nonlinear parabolic problem is proposed. The standard Galerkin finite element method based on P2 conforming elements is used to the spatial discretization of the problem and the Crank-Nicolson/Newton scheme is applied to the time discretization of the resulted finite element equations. Moreover, assuming the appropriate regularity of the exact solution and the finite element solution, we obtain optimal error estimates of the fully discrete Crank-Nicolson/Newton scheme of nonlinear parabolic problem. Finally, numerical experiments are presented to show the effcient performance of the proposed scheme.
Asymptotic solution for a class of weakly nonlinear singularly perturbed reaction diffusion problem
Institute of Scientific and Technical Information of China (English)
TANG Rong-rong
2009-01-01
Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter e and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of O(ε2).
Institute of Scientific and Technical Information of China (English)
鲁世平
2003-01-01
By employing the theory of differential inequality and some analysis methods, a nonlinear boundary value problem subject to a general kind of second-order Volterra functional differential equation was considered first. Then, by constructing the right-side layer function and the outer solution, a nonlinear boundary value problem subject to a kind of second- order Volterra functional differential equation with a small parameter was studied further. By using the differential mean value theorem and the technique of upper and lower solution, a new result on the existence of the solutions to the boundary value problem is obtained, and a uniformly valid asymptotic expansions of the solution is given as well.
A Symmetric Characteristic Finite Volume Element Scheme for Nonlinear Convection-Diffusion Problems
Institute of Scientific and Technical Information of China (English)
Min Yang; Yi-rang Yuan
2008-01-01
In this paper, we implement alternating direction strategy and construct a symmetric FVE scheme for nonlinear convection-diffusion problems. Comparing to general FVE methods, our method has two advantages. First, the coefficient matrices of the discrete schemes will be symmetric even for nonlinear problems.Second, since the solution of the algebraic equations at each time step can be inverted into the solution of several one-dimensional problems, the amount of computation work is smaller. We prove the optimal H1-norm error estimates of order O(△t2 + h) and present some numerical examples at the end of the paper.
Directory of Open Access Journals (Sweden)
Alain Mignot
2005-09-01
Full Text Available This paper shows the existence of a solution of the quasi-static unilateral contact problem with nonlocal friction law for nonlinear elastic materials. We set up a variational incremental problem which admits a solution, when the friction coefficient is small enough, and then by passing to the limit with respect to time we obtain a solution.
Regularization method with two parameters for nonlinear ill-posed problems
Institute of Scientific and Technical Information of China (English)
2008-01-01
This paper is devoted to the regularization of a class of nonlinear ill-posed problems in Banach spaces. The operators involved are multi-valued and the data are assumed to be known approximately. Under the assumption that the original problem is solvable, a strongly convergent approximation procedure is designed by means of the Tikhonov regularization method with two pa- rameters.
A Smooth Newton Method for Nonlinear Programming Problems with Inequality Constraints
Directory of Open Access Journals (Sweden)
Vasile Moraru
2012-02-01
Full Text Available The paper presents a reformulation of the Karush-Kuhn-Tucker (KKT system associated nonlinear programming problem into an equivalent system of smooth equations. Classical Newton method is applied to solve the system of equations. The superlinear convergence of the primal sequence, generated by proposed method, is proved. The preliminary numerical results with a problems test set are presented.
Multipoint Singular Boundary-Value Problem for Systems of Nonlinear Differential Equations
Directory of Open Access Journals (Sweden)
Zdeněk Šmarda
2009-01-01
Full Text Available A singular Cauchy-Nicoletti problem for a system of nonlinear ordinary differential equations is considered. With the aid of combination of Ważewski's topological method and Schauder's principle, the theorem concerning the existence of a solution of this problem (having the graph in a prescribed domain is proved.
COYOTE: a finite-element computer program for nonlinear heat-conduction problems
Energy Technology Data Exchange (ETDEWEB)
Gartling, D.K.
1982-10-01
COYOTE is a finite element computer program designed for the solution of two-dimensional, nonlinear heat conduction problems. The theoretical and mathematical basis used to develop the code is described. Program capabilities and complete user instructions are presented. Several example problems are described in detail to demonstrate the use of the program.
Existence of Solutions for Nonlinear Four-Point -Laplacian Boundary Value Problems on Time Scales
Directory of Open Access Journals (Sweden)
Topal SGulsan
2009-01-01
Full Text Available We are concerned with proving the existence of positive solutions of a nonlinear second-order four-point boundary value problem with a -Laplacian operator on time scales. The proofs are based on the fixed point theorems concerning cones in a Banach space. Existence result for -Laplacian boundary value problem is also given by the monotone method.
The Cauchy problem for non-autonomous nonlinear Schr(o)dinger equations
Institute of Scientific and Technical Information of China (English)
Peter Y. H. Pang; TANG Hongyan; WANG Youde
2005-01-01
In this paper we study the Cauchy problem for cubic nonlinear Schr(o)dinger equation with space-and time-dependent coefficients on Rm and Tm. By an approximation argument we prove that for suitable initial values, the Cauchy problem admits unique local solutions. Global existence is discussed in the cases of m=1,2.
On high-continuity transfinite element formulations for linear-nonlinear transient thermal problems
Tamma, Kumar K.; Railkar, Sudhir B.
1987-01-01
This paper describes recent developments in the applicability of a hybrid transfinite element methodology with emphasis on high-continuity formulations for linear/nonlinear transient thermal problems. The proposed concepts furnish accurate temperature distributions and temperature gradients making use of a relatively smaller number of degrees of freedom; and the methodology is applicable to linear/nonlinear thermal problems. Characteristic features of the formulations are described in technical detail as the proposed hybrid approach combines the major advantages and modeling features of high-continuity thermal finite elements in conjunction with transform methods and classical Galerkin schemes. Several numerical test problems are evaluated and the results obtained validate the proposed concepts for linear/nonlinear thermal problems.
SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis
Energy Technology Data Exchange (ETDEWEB)
Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.
1998-08-01
This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. The notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.
Cauchy problem for a class of nonlinear dispersive wave equations arising in elasto-plastic flow
Zhijian, Yang
2006-01-01
The paper studies the existence, both locally and globally in time, stability, decay estimates and blowup of solutions to the Cauchy problem for a class of nonlinear dispersive wave equations arising in elasto-plastic flow. Under the assumption that the nonlinear term of the equations is of polynomial growth order, say [alpha], it proves that when [alpha]>1, the Cauchy problem admits a unique local solution, which is stable and can be continued to a global solution under rather mild conditions; when [alpha][greater-or-equal, slanted]5 and the initial data is small enough, the Cauchy problem admits a unique global solution and its norm in L1,p(R) decays at the rate for 2
nonlinear term, the local solutions of the Cauchy problem blow up in finite time.
Cross-constrained problems for nonlinear Schrodinger equation with harmonic potential
Directory of Open Access Journals (Sweden)
Runzhang Xu
2012-11-01
Full Text Available This article studies a nonlinear Schodinger equation with harmonic potential by constructing different cross-constrained problems. By comparing the different cross-constrained problems, we derive different sharp criterion and different invariant manifolds that separate the global solutions and blowup solutions. Moreover, we conclude that some manifolds are empty due to the essence of the cross-constrained problems. Besides, we compare the three cross-constrained problems and the three depths of the potential wells. In this way, we explain the gaps in [J. Shu and J. Zhang, Nonlinear Shrodinger equation with harmonic potential, Journal of Mathematical Physics, 47, 063503 (2006], which was pointed out in [R. Xu and Y. Liu, Remarks on nonlinear Schrodinger equation with harmonic potential, Journal of Mathematical Physics, 49, 043512 (2008].
A NUMERICAL METHOD FOR SIMULATING NONLINEAR FLUID-RIGID STRUCTURE INTERACTION PROBLEMS
Institute of Scientific and Technical Information of China (English)
XingJ.T; PriceW.G; ChenY.G
2005-01-01
A numerical method for simulating nonlinear fluid-rigid structure interaction problems is developed. The structure is assumed to undergo large rigid body motions and the fluid flow is governed by nonlinear, viscous or non-viscous, field equations with nonlinear boundary conditions applied to the free surface and fluid-solid interaction interfaces. An Arbitrary-Lagrangian-Eulerian (ALE) mesh system is used to construct the numerical model. A multi-block numerical scheme of study is adopted allowing for the relative motion between moving overset grids, which are independent of one another. This provides a convenient method to overcome the difficulties in matching fluid meshes with large solid motions. Nonlinear numerical equations describing nonlinear fluid-solid interaction dynamics are derived through a numerical discretization scheme of study. A coupling iteration process is used to solve these numerical equations. Numerical examples are presented to demonstrate applications of the model developed.
TOEPLITZ OPERATORS AND ALGEBRAS ON DIRICHLET SPACES
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The automorphism group of the Toeplitz C*- algebra,J(C1),generated by Toeplitz operators with C1-symbols on Dirichlet space D is discussed; the K0,K1-groups and the first cohomology group of J(C1) are computed.In addition,the author proves that the spectra of Toeplitz operators with C1-symbols are always connected,and discusses the algebraic properties of Toeplitz operators.In particular,it is proved that there is no nontrivial selfadjoint Toeplitz operator on D and T* = T if and only if T is a scalar operator.
Modeling Word Burstiness Using the Dirichlet Distribution
DEFF Research Database (Denmark)
Madsen, Rasmus Elsborg; Kauchak, David; Elkan, Charles
2005-01-01
Multinomial distributions are often used to model text documents. However, they do not capture well the phenomenon that words in a document tend to appear in bursts: if a word appears once, it is more likely to appear again. In this paper, we propose the Dirichlet compound multinomial model (DCM......) as an alternative to the multinomial. The DCM model has one additional degree of freedom, which allows it to capture burstiness. We show experimentally that the DCM is substantially better than the multinomial at modeling text data, measured by perplexity. We also show using three standard document collections...
A Weak Solution of a Stochastic Nonlinear Problem
Directory of Open Access Journals (Sweden)
M. L. Hadji
2015-01-01
Full Text Available We consider a problem modeling a porous medium with a random perturbation. This model occurs in many applications such as biology, medical sciences, oil exploitation, and chemical engineering. Many authors focused their study mostly on the deterministic case. The more classical one was due to Biot in the 50s, where he suggested to ignore everything that happens at the microscopic level, to apply the principles of the continuum mechanics at the macroscopic level. Here we consider a stochastic problem, that is, a problem with a random perturbation. First we prove a result on the existence and uniqueness of the solution, by making use of the weak formulation. Furthermore, we use a numerical scheme based on finite differences to present numerical results.
Institute of Scientific and Technical Information of China (English)
Jeong Ja Bae
2012-01-01
In this article,we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physically different types of materials,one component is a Kirchhoff type wave equation with nonlinear time dependent localized dissipation which is effective only on a neighborhood of certain part of the boundary,while the other is a Kirchhoff type wave equation with nonlinear memory.
An Efficient Pseudospectral Method for Solving a Class of Nonlinear Optimal Control Problems
Emran Tohidi; Atena Pasban; Kilicman, A.; S. Lotfi Noghabi
2013-01-01
This paper gives a robust pseudospectral scheme for solving a class of nonlinear optimal control problems (OCPs) governed by differential inclusions. The basic idea includes two major stages. At the first stage, we linearize the nonlinear dynamical system by an interesting technique which is called linear combination property of intervals. After this stage, the linearized dynamical system is transformed into a multi domain dynamical system via computational interval partitioning. Moreover,...
Institute of Scientific and Technical Information of China (English)
TAO Hua-xue; GUO Jin-yun
2005-01-01
The unknown parameter's variance-covariance propagation and calculation in the generalized nonlinear least squares remain to be studied now,which didn't appear in the internal and external referencing documents. The unknown parameter's variance-covariance propagation formula, considering the two-power terms, was concluded used to evaluate the accuracy of unknown parameter estimators in the generalized nonlinear least squares problem. It is a new variance-covariance formula and opens up a new way to evaluate the accuracy when processing data which have the multi-source,multi-dimensional, multi-type, multi-time-state, different accuracy and nonlinearity.
Application of HPEM to investigate the response and stability of nonlinear problems in vibration
DEFF Research Database (Denmark)
Mohammadi, M.H.; Mohammadi, A.; Kimiaeifar, A.
2010-01-01
In this work, a powerful analytical method, called He's Parameter Expanding Methods (HPEM) is used to obtain the exact solution of nonlinear problems in nonlinear vibration. In this work, the governing equation is obtained by using Lagrange method, then the nonlinear governing equation is solved...... analytically by He's Parameter Expanding Methods. It is shown that one term in series expansions is sufficient to obtain a highly accurate solution which is valid for the whole domain. Comparison of the obtained solutions with those obtained using numerical method shows that this method is effective...
SOME BOUNDARY VALUE PROBLEMS FOR NONLINEAR DEGENERATE ELLIPTIC EQUATIONS OF SECOND ORDER
Institute of Scientific and Technical Information of China (English)
Wen Guochun
2007-01-01
The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem. Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension, the existence of solutions of the above problem is proved. In this article, the complex analytic method is used, namely the corresponding problem for degenerate elliptic complex equations of first order is firstly discussed, afterwards the above problem for the degenerate elliptic equations of second order is solved.
OBLIQUE DERIVATIVE PROBLEMS FOR SECOND ORDER NONLINEAR MIXED EQUATIONS WITH DEGENERATE LINE
Institute of Scientific and Technical Information of China (English)
Wen Guochun
2008-01-01
The present article deals with oblique derivative problems for some nonlin-ear mixed equations with parabolic degeneracy, which include the Tricomi problem as a special case. First, the formulation of the problems for the equations is given; next, the representation and estimates of solutions for the above problems are obtained; finally, the existence of solutions for the problems is proved by the successive iteration and the com-pactness principle of solutions of the problems. In this article, the author uses the complex method, namely, the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used.
A monotonic method for solving nonlinear optimal control problems
Salomon, Julien
2009-01-01
Initially introduced in the framework of quantum control, the so-called monotonic algorithms have shown excellent numerical results when dealing with various bilinear optimal control problems. This paper aims at presenting a unified formulation of such procedures and the intrinsic assumptions they require. In this framework, we prove the feasibility of the general algorithm. Finally, we explain how these assumptions can be relaxed.
Optimal Control Problems for Nonlinear Variational Evolution Inequalities
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Eun-Young Ju
2013-01-01
Full Text Available We deal with optimal control problems governed by semilinear parabolic type equations and in particular described by variational inequalities. We will also characterize the optimal controls by giving necessary conditions for optimality by proving the Gâteaux differentiability of solution mapping on control variables.
A-monotonicity and applications to nonlinear variational inclusion problems
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Ram U. Verma
2004-01-01
Full Text Available A new notion of the A-monotonicity is introduced, which generalizes the H-monotonicity. Since the A-monotonicity originates from hemivariational inequalities, and hemivariational inequalities are connected with nonconvex energy functions, it turns out to be a useful tool proving the existence of solutions of nonconvex constrained problems as well.
THE PITS PROPERTY OF ENTIRE FUNCTIONS DEFINED BY DIRICHLET SERIES
Institute of Scientific and Technical Information of China (English)
Shang Lina; Gao Zongsheng
2009-01-01
The value distribution of entire functions defined by Dirichlet series are studied in this present article. It is proved that entire functions defined by Dirichlet series have the pits property, which improve the relative results on lacunary Taylor series obtained by Littlewood J.E. and Offord A.C.
Some comparison of restarted GMRES and QMR for linear and nonlinear problems
Energy Technology Data Exchange (ETDEWEB)
Morgan, R. [Baylor Univ., Waco, TX (United States); Joubert, W. [Los Alamos National Lab., NM (United States)
1994-12-31
Comparisons are made between the following methods: QMR including its transpose-free version, restarted GMRES, and a modified restarted GMRES that uses approximate eigenvectors to improve convergence, For some problems, the modified GMRES is competitive with or better than QMR in terms of the number of matrix-vector products. Also, the GMRES methods can be much better when several similar systems of linear equations must be solved, as in the case of nonlinear problems and ODE problems.
A NONLOCAL NONLINEAR BOUNDARY VALUE PROBLEM FOR THE HEAT EQUATIONS
Institute of Scientific and Technical Information of China (English)
YANJINHAI
1996-01-01
The existenoe and limit hehaviour of the solution for a kind of nonloeal noulinear boundary value condition on a part of the boundary is studied for the heat equation, which physicallymeans that the potential is the function of the total flux. When this part of boundary shrinks to a point in a certain way, this condition either results in a Dirac measure or simply disappears in the corresponding problem.
Nodal Solutions for a Nonlinear Fourth-Order Eigenvalue Problem
Institute of Scientific and Technical Information of China (English)
Ru Yun MA; Bevan THOMPSON
2008-01-01
We are concerned with determining the values of λ, for which there exist nodal solutions of the fourth-order boundary value problem y =λa(x)f(y),00 for all u ≠0. We give conditions on the ratio f (s)/s,at infinity and zero, that guarantee the existence of nodal solutions.The proof of our main results is based upon bifurcation techniques.
Fast Inverse Nonlinear Fourier Transforms for Fiber Bragg Grating Design and Related Problems
Wahls, Sander
2016-01-01
The problem of constructing a fiber Bragg grating profile numerically such that the reflection coefficient of the grating matches a given specification is considered. The well-known analytic solution to this problem is given by a suitable inverse nonlinear Fourier transform (also known as inverse scattering transform) of the specificed reflection coefficient. Many different algorithms have been proposed to compute this inverse nonlinear Fourier transform numerically. The most efficient ones require $\\mathcal{O}(D^{2})$ floating point operations (flops) to generate $D$ samples of the grating profile. In this paper, two new fast inverse nonlinear Fourier transform algorithms that require only $\\mathcal{O}(D\\log^{2}D)$ flops are proposed. The merits of our algorithms are demonstrated in numerical examples, in which they are compared to a conventional layer peeling method, the Toeplitz inner bordering method and integral layer peeling. One of our two algorithms also extends to the design problem for fiber-assiste...
Application of a new method of nonlinear dynamical system identification to biochemical problems.
Karnaukhov, A V; Karnaukhova, E V
2003-03-01
The system identification method for a variety of nonlinear dynamic models is elaborated. The problem of identification of an original nonlinear model presented as a system of ordinary differential equations in the Cauchy explicit form with a polynomial right part reduces to the solution of the system of linear equations for the constants of the dynamical model. In other words, to construct an integral model of the complex system (phenomenon), it is enough to collect some data array characterizing the time-course of dynamical parameters of the system. Collection of such a data array has always been a problem. However difficulties emerging are, as a rule, not principal and may be overcome almost without exception. The potentialities of the method under discussion are demonstrated by the example of the test problem of multiparametric nonlinear oscillator identification. The identification method proposed may be applied to the study of different biological systems and in particular the enzyme kinetics of complex biochemical reactions.
Directory of Open Access Journals (Sweden)
Paras Bhatnagar
2012-10-01
Full Text Available Kaul and Kaur [7] obtained necessary optimality conditions for a non-linear programming problem by taking the objective and constraint functions to be semilocally convex and their right differentials at a point to be lower semi-continuous. Suneja and Gupta [12] established the necessary optimality conditions without assuming the semilocal convexity of the objective and constraint functions but their right differentials at the optimal point to be convex. Suneja and Gupta [13] established necessary optimality conditions for an efficient solution of a multiobjective non-linear programming problem by taking the right differentials of the objective functions and constraintfunctions at the efficient point to be convex. In this paper we obtain some results for a properly efficient solution of a multiobjective non-linear fractional programming problem involving semilocally convex and related functions by assuming generalized Slater type constraint qualification.
Directory of Open Access Journals (Sweden)
Suxiang He
2014-01-01
Full Text Available An implementable nonlinear Lagrange algorithm for stochastic minimax problems is presented based on sample average approximation method in this paper, in which the second step minimizes a nonlinear Lagrange function with sample average approximation functions of original functions and the sample average approximation of the Lagrange multiplier is adopted. Under a set of mild assumptions, it is proven that the sequences of solution and multiplier obtained by the proposed algorithm converge to the Kuhn-Tucker pair of the original problem with probability one as the sample size increases. At last, the numerical experiments for five test examples are performed and the numerical results indicate that the algorithm is promising.
The Modified Adomian Decomposition Method for Nonlinear Fractional Boundary Value Problems
Institute of Scientific and Technical Information of China (English)
WANG Jie
2012-01-01
We use the modified Adomian decomposition method(ADM) for solving the nonlinear fractional boundary value problem Dα0+u(x)=f(x,u(x)), 0＜x＜1, 3＜α≤4u(0) =α0, u″(0) =α2 (1)u(1) =β0, u″(1) =β2where Dα0+u is Caputo fractional derivative and α0,α2,β0,β2 is not zero at all,and f:[0,1] x R → R is continuous.The calculated numerical results show reliability and efficiency of the algorithm given.The numerical procedure is tested on linear and nonlinear problems.
ASYMPTOTIC THEORY OF INITIAL VALUE PROBLEMS FOR NONLINEAR PERTURBED KLEIN-GORDON EQUATIONS
Institute of Scientific and Technical Information of China (English)
GAN Zai-hui; ZHANG Jian
2005-01-01
The asymptotic theory of initial value problems for a class of nonlinear perturbed Klein-Gordon equations in two space dimensions is considered. Firstly, using the contraction mapping principle, combining some priori estimates and the convergence of Bessel function, the well-posedness of solutions of the initial value problem in twice continuous differentiable space was obtained according to the equivalent integral equation of initial value problem for the Klein-Gordon equations. Next, formal approximations of initial value problem was constructed by perturbation method and the asymptotic validity of the formal approximation is got. Finally, an application of the asymptotic theory was given, the asymptotic approximation degree of solutions for the initial value problem of a specific nonlinear Klein-Gordon equation was analyzed by using the asymptotic approximation theorem.
Minimization of the k-th eigenvalue of the Dirichlet Laplacian
Bucur, Dorin
2012-12-01
For every {k in {N}}, we prove the existence of a quasi-open set minimizing the k-th eigenvalue of the Dirichlet Laplacian among all sets of prescribed Lebesgue measure. Moreover, we prove that every minimizer is bounded and has a finite perimeter. The key point is the observation that such quasi-open sets are shape subsolutions for an energy minimizing free boundary problem.
A boundary control problem with a nonlinear reaction term
Directory of Open Access Journals (Sweden)
John R. Cannon
2009-04-01
Full Text Available The authors study the problem $u_t=u_{xx}-au$, $0
Kounadis, A. N.
1992-05-01
An efficient and easily applicable, approximate analytic technique for the solution of nonlinear initial and boundary-value problems associated with nonlinear ordinary differential equations (O.D.E.) of any order and variable coefficients, is presented. Convergence, uniqueness and upper bound error estimates of solutions, obtained by the successive approximations scheme of the proposed technique, are thoroughly established. Important conclusions regarding the improvement of convergence for large time and large displacement solutions in case of nonlinear initial-value problems are also assessed. The proposed technique is much more efficient than the perturbations schemes for establishing the large postbuckling response of structural systems. The efficiency, simplicity and reliability of the proposed technique is demonstrated by two illustrative examples for which available numerical results exist.
Directory of Open Access Journals (Sweden)
Bonić Zoran
2010-01-01
Full Text Available The paper presents application of nonlinear material models in the software package Ansys. The development of the model theory is presented in the paper of the mathematical modeling of material nonlinear problems in structural analysis (part I - theoretical foundations, and here is described incremental-iterative procedure for solving problems of nonlinear material used by this package and an example of modeling of spread footing by using Bilinear-kinematics and Drucker-Prager mode was given. A comparative analysis of the results obtained by these modeling and experimental research of the author was made. Occurrence of the load level that corresponds to plastic deformation was noted, development of deformations with increasing load, as well as the distribution of dilatation in the footing was observed. Comparison of calculated and measured values of reinforcement dilatation shows their very good agreement.
Analysis of search-extension method for finding multiple solutions of nonlinear problem
Institute of Scientific and Technical Information of China (English)
2008-01-01
For numerical computations of multiple solutions of the nonlinear elliptic problemΔu+ f（u）=0 inΩ, u=0 onΓ, a search-extension method （SEM） was proposed and systematically studied by the authors. This paper shall complete its theoretical analysis. It is assumed that the nonlinearity is non-convex and its solution is isolated, under some conditions the corresponding linearized problem has a unique solution. By use of the compactness of the solution family and the contradiction argument, in general conditions, the high order regularity of the solution u∈H1+α,α>0 is proved. Assume that some initial value searched by suitably many eigenbases is already fallen into the neighborhood of the isolated solution, then the optimal error estimates of its nonlinear finite element approximation are shown by the duality argument and continuation method.
Unsupervised Feature Selection for Latent Dirichlet Allocation
Institute of Scientific and Technical Information of China (English)
Xu Weiran; Du Gang; Chen Guang; Guo Jun; Yang Jie
2011-01-01
As a generative model Latent Dirichlet Allocation Model,which lacks optimization of topics' discrimination capability focuses on how to generate data,This paper aims to improve the discrimination capability through unsupervised feature selection.Theoretical analysis shows that the discrimination capability of a topic is limited by the discrimination capability of its representative words.The discrimination capability of a word is approximated by the Information Gain of the word for topics,which is used to distinguish between “general word” and “special word” in LDA topics.Therefore,we add a constraint to the LDA objective function to let the “general words” only happen in “general topics”other than “special topics”.Then a heuristic algorithm is presented to get the solution.Experiments show that this method can not only improve the information gain of topics,but also make the topics easier to understand by human.
Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces
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Cho Yeol
2011-01-01
Full Text Available Abstract In this paper, the existing theorems and methods for finding solutions of systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces are studied. To overcome the difficulties, due to the presence of a proper convex lower semi-continuous function, φ and a mapping g, which appeared in the considered problem, we have used some applications of the resolvent operator technique. We would like to point out that although many authors have proved results for finding solutions of the systems of nonlinear set-valued (mixed variational inequalities problems, it is clear that it cannot be directly applied to the problems that we have considered in this paper because of φ and g. 2000 AMS Subject Classification: 47H05; 47H09; 47J25; 65J15.
Roul, Pradip
2016-06-01
This paper presents a new iterative technique for solving nonlinear singular two-point boundary value problems with Neumann and Robin boundary conditions. The method is based on the homotopy perturbation method and the integral equation formalism in which a recursive scheme is established for the components of the approximate series solution. This method does not involve solution of a sequence of nonlinear algebraic or transcendental equations for the unknown coefficients as in some other iterative techniques developed for singular boundary value problems. The convergence result for the proposed method is established in the paper. The method is illustrated by four numerical examples, two of which have physical significance: The first problem is an application of the reaction-diffusion process in a porous spherical catalyst and the second problem arises in the study of steady-state oxygen-diffusion in a spherical cell with Michaelis-Menten uptake kinetics.
A high-performance feedback neural network for solving convex nonlinear programming problems.
Leung, Yee; Chen, Kai-Zhou; Gao, Xing-Bao
2003-01-01
Based on a new idea of successive approximation, this paper proposes a high-performance feedback neural network model for solving convex nonlinear programming problems. Differing from existing neural network optimization models, no dual variables, penalty parameters, or Lagrange multipliers are involved in the proposed network. It has the least number of state variables and is very simple in structure. In particular, the proposed network has better asymptotic stability. For an arbitrarily given initial point, the trajectory of the network converges to an optimal solution of the convex nonlinear programming problem under no more than the standard assumptions. In addition, the network can also solve linear programming and convex quadratic programming problems, and the new idea of a feedback network may be used to solve other optimization problems. Feasibility and efficiency are also substantiated by simulation examples.
The solution of singular optimal control problems using direct collocation and nonlinear programming
Downey, James R.; Conway, Bruce A.
1992-08-01
This paper describes work on the determination of optimal rocket trajectories which may include singular arcs. In recent years direct collocation and nonlinear programming has proven to be a powerful method for solving optimal control problems. Difficulties in the application of this method can occur if the problem is singular. Techniques exist for solving singular problems indirectly using the associated adjoint formulation. Unfortunately, the adjoints are not a part of the direct formulation. It is shown how adjoint information can be obtained from the direct method to allow the solution of singular problems.
Long step homogeneous interior point algorithm for the p* nonlinear complementarity problems
Directory of Open Access Journals (Sweden)
Lešaja Goran
2002-01-01
Full Text Available A P*-Nonlinear Complementarity Problem as a generalization of the P*-Linear Complementarity Problem is considered. We show that the long-step version of the homogeneous self-dual interior-point algorithm could be used to solve such a problem. The algorithm achieves linear global convergence and quadratic local convergence under the following assumptions: the function satisfies a modified scaled Lipschitz condition, the problem has a strictly complementary solution, and certain submatrix of the Jacobian is nonsingular on some compact set.
Institute of Scientific and Technical Information of China (English)
Jingsun Yao; Jiaqi Mo
2005-01-01
The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
A smart nonstandard finite difference scheme for second order nonlinear boundary value problems
Erdogan, Utku; Ozis, Turgut
2011-01-01
A new kind of finite difference scheme is presented for special second order nonlinear two point boundary value problems. An artificial parameter is introduced in the scheme. Symbolic computation is proposed for the construction of the scheme. Local truncation error of the method is discussed. Numer
ON THE NONLINEAR RIEMANN PROBLEMS FOR GENERAL FIRST ELLIPTIC SYSTEMS IN THE PLANE
Institute of Scientific and Technical Information of China (English)
李明忠; 宋洁
2005-01-01
The nonlinear Riemann problem for general systems of the first-order linear and quasi-linear equations in the plane are considered. It translates them to singular integral equations and proves the existence of the solution by means of contract principle or. general contract principle. The known results are generalized.
On the solvability of initial-value problems for nonlinear implicit difference equations
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Yen Ha Thi Ngoc
2004-01-01
Full Text Available Our aim is twofold. First, we propose a natural definition of index for linear nonautonomous implicit difference equations, which is similar to that of linear differential-algebraic equations. Then we extend this index notion to a class of nonlinear implicit difference equations and prove some existence theorems for their initial-value problems.
THE CAUCHY PROBLEM OF NONLINEAR SCHR(O)DINGER-BOUSSINESQ EQUATIONS IN Hs(Rd)
Institute of Scientific and Technical Information of China (English)
Han Yongqian
2005-01-01
In this paper, the local well posedness and global well posedness of solutions for the initial value problem (IVP) of nonlinear Schrodinger-Boussinesq equations is considered in Hs(Rd) by resorting Besov spaces, where real number s ≥ 0.
On the solvability of initial-value problems for nonlinear implicit difference equations
Directory of Open Access Journals (Sweden)
Ha Thi Ngoc Yen
2004-07-01
Full Text Available Our aim is twofold. First, we propose a natural definition of index for linear nonautonomous implicit difference equations, which is similar to that of linear differential-algebraic equations. Then we extend this index notion to a class of nonlinear implicit difference equations and prove some existence theorems for their initial-value problems.
A smart nonstandard finite difference scheme for second order nonlinear boundary value problems
Erdogan, Utku; Ozis, Turgut
2011-01-01
A new kind of finite difference scheme is presented for special second order nonlinear two point boundary value problems. An artificial parameter is introduced in the scheme. Symbolic computation is proposed for the construction of the scheme. Local truncation error of the method is discussed.
Solutions of Multi Objective Fuzzy Transportation Problems with Non-Linear Membership Functions
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Dr. M. S. Annie Christi
2016-11-01
Full Text Available Multi-objective transportation problem with fuzzy interval numbers are considered. The solution of linear MOTP is obtained by using non-linear membership functions. The optimal compromise solution obtained is compared with the solution got by using a linear membership function. Some numerical examples are presented to illustrate this.
Nonlinear quarter-plane problem for the Korteweg-de Vries equation
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Nikolai A. Larkin
2011-08-01
Full Text Available This article concerns an initial-boundary value problem in a quarter-plane for the Korteweg-de Vries (KdV equation. For general nonlinear boundary conditions we prove the existence and uniqueness of a global regular solution.
Institute of Scientific and Technical Information of China (English)
Yepeng Xing; Qiong Wang; Valery G. Romanovski
2009-01-01
We prove several new comparison results and develop the monotone iterative tech-nique to show the existence of extremal solutions to a kind of periodic boundary value problem (PBVP) for nonlinear integro-differential equation of mixed type on time scales.
Positive Solutions of a Nonlinear Fourth-order Integral Boundary Value Problem
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Benaicha Slimane
2016-07-01
Full Text Available In this paper, the existence of positive solutions for a nonlinear fourth-order two-point boundary value problem with integral condition is investigated. By using Krasnoselskii’s fixed point theorem on cones, sufficient conditions for the existence of at least one positive solutions are obtained.
THE NONLINEAR BOUNDARY VALUE PROBLEM FOR A CLASS OF INTEGRO-DIFFERENTIAL SYSTEM
Institute of Scientific and Technical Information of China (English)
Rongrong Tang
2006-01-01
In this paper, using the theory of differential inequalities, we study the nonlinear boundary value problem for a class of integro-differential system. Under appropriate assumptions, the existence of solution is proved and the uniformly valid asymptotic expansions for arbitrary n-th order approximation and the estimation of remainder term are obtained simply and conveniently.
Scenarios for solving a non-linear transportation problem in multi-agent systems
DEFF Research Database (Denmark)
Brehm, Robert; Top, Søren; Mátéfi-Tempfli, Stefan
2017-01-01
We introduce and provide an evaluation on two scenarios and related algorithms for implementation of a multi-agent system to solve a type of non-linear transportation problem using distributed optimization algorithms based on dual decomposition and consensus. The underlying fundamental optimization...
EXISTENCE AND UNIQUENESS RESULTS FOR NONLINEAR THIRD-ORDER BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper,we investigate a nonlinear third-order three-point boundary value problem. By several well-known fixed point theorems,the existence of positive solutions is discussed. Besides,the uniqueness results are obtained by imposing growth restrictions on f.
Institute of Scientific and Technical Information of China (English)
Yaohong LI; Xiaoyan ZHANG
2013-01-01
In this paper,we consider boundary value problems for systems of nonlinear thirdorder differential equations.By applying the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed point theorem,the existence of multiple positive solutions is obtained.As application,we give some examples to demonstrate our results.
Existence of three solutions for impulsive nonlinear fractional boundary value problems
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Shapour Heidarkhani
2017-01-01
Full Text Available In this work we present new criteria on the existence of three solutions for a class of impulsive nonlinear fractional boundary-value problems depending on two parameters. We use variational methods for smooth functionals defined on reflexive Banach spaces in order to achieve our results.
Existence of Two Solutions of Nonlinear m-Point Boundary Value Problems
Institute of Scientific and Technical Information of China (English)
任景莉; 葛渭高
2003-01-01
Sufficient conditions for the existence of at least two positive solutions of a nonlinear m-points boundary value problems are established. The results are obtained by using a new fixed point theorem in cones. An example is provided to illustrate the theory.
Institute of Scientific and Technical Information of China (English)
CHENGYan
2003-01-01
In this paper,the fixed-point theorem is used to estimated an asymptotic solution of intial val-ue problems for a class of third nonlinear differential equations which has double initial-layer properties.We obtain the uniformly valid asymptotic expansion of any orders including boundary layers.
A two-phase free boundary problem for a nonlinear diffusion-convection equation
Energy Technology Data Exchange (ETDEWEB)
De Lillo, S; Lupo, G [Dipartimento di Matematica e Informatica, Universita degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia (Italy)], E-mail: silvana.delillo@pg.infn.it
2008-04-11
A two-phase free boundary problem associated with a diffusion-convection equation is considered. The problem is reduced to a system of nonlinear integral equations, which admits a unique solution for small times. The system admits an explicit two-component solution corresponding to a two-component shock wave of the Burgers equation. The stability of such a solution is also discussed.
Nonlinear boundary value problems for first order impulsive integro-differential equations
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Xinzhi Liu
1989-01-01
Full Text Available In this paper, we investigate a class of first order impulsive integro-differential equations subject to certain nonlinear boundary conditions and prove, with the help of upper and lower solutions, that the problem has a solution lying between the upper and lower solutions. We also develop monotone iterative technique and show the existence of multiple solutions of a class of periodic boundary value problems.
On the System of Nonlinear Mixed Implicit Equilibrium Problems in Hilbert Spaces
Directory of Open Access Journals (Sweden)
Yeol Je Cho
2010-01-01
Full Text Available We use the Wiener-Hopf equations and the Yosida approximation notions to prove the existence theorem of a system of nonlinear mixed implicit equilibrium problems (SMIE in Hilbert spaces. The algorithm for finding a solution of the problem (SMIE is suggested; the convergence criteria and stability of the iterative algorithm are discussed. The results presented in this paper are more general and are viewed as an extension, refinement, and improvement of the previously known results in the literature.
Directory of Open Access Journals (Sweden)
Xiaofei Cao
2016-11-01
Full Text Available In this article, we consider the multiplicity of positive solutions for a class of Kirchhoff type problems with concave and convex nonlinearities. Under appropriate assumptions, we prove that the problem has at least two positive solutions, moreover, one of which is a positive ground state solution. Our approach is mainly based on the Nehari manifold, Ekeland variational principle and the theory of Lagrange multipliers.
Error estimations of mixed finite element methods for nonlinear problems of shallow shell theory
Karchevsky, M.
2016-11-01
The variational formulations of problems of equilibrium of a shallow shell in the framework of the geometrically and physically nonlinear theory by boundary conditions of different main types, including non-classical, are considered. Necessary and sufficient conditions for their solvability are derived. Mixed finite element methods for the approximate solutions to these problems based on the use of second derivatives of the bending as auxiliary variables are proposed. Estimations of accuracy of approximate solutions are established.
Initial value problem for a class of fourth-order nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
Guo-wang CHEN; Chang-shun HOU
2009-01-01
In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractional order Sobolev space using the contraction mapping principle and the extension theorem. The sufficient conditions for the blow up of the solution to the initial value problem are given.
On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation
Directory of Open Access Journals (Sweden)
Said Mesloub
2008-03-01
Full Text Available This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the regularity of a solution.
On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation
Directory of Open Access Journals (Sweden)
Mesloub Said
2008-01-01
Full Text Available This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the regularity of a solution.
A second eigenvalue bound for the Dirichlet Schrodinger equation wtih a radially symmetric potential
Directory of Open Access Journals (Sweden)
Craig Haile
2000-01-01
Full Text Available We study the time-independent Schrodinger equation with radially symmetric potential $k|x|^alpha$, $k ge 0$, $k in mathbb{R}, alpha ge 2$ on a bounded domain $Omega$ in $mathbb{R}^n$, $(n ge 2$ with Dirichlet boundary conditions. In particular, we compare the eigenvalue $lambda_2(Omega$ of the operator $-Delta + k |x|^alpha $ on $Omega$ with the eigenvalue $lambda_2(S_1$ of the same operator $-Delta +kr^alpha$ on a ball $S_1$, where $S_1$ has radius such that the first eigenvalues are the same ($lambda_1(Omega = lambda_1(S_1$. The main result is to show $lambda_2(Omega le lambda_2(S_1$. We also give an extension of the main result to the case of a more general elliptic eigenvalue problem on a bounded domain $Omega$ with Dirichlet boundary conditions.
On selecting a prior for the precision parameter of Dirichlet process mixture models
Dorazio, R.M.
2009-01-01
In hierarchical mixture models the Dirichlet process is used to specify latent patterns of heterogeneity, particularly when the distribution of latent parameters is thought to be clustered (multimodal). The parameters of a Dirichlet process include a precision parameter ?? and a base probability measure G0. In problems where ?? is unknown and must be estimated, inferences about the level of clustering can be sensitive to the choice of prior assumed for ??. In this paper an approach is developed for computing a prior for the precision parameter ?? that can be used in the presence or absence of prior information about the level of clustering. This approach is illustrated in an analysis of counts of stream fishes. The results of this fully Bayesian analysis are compared with an empirical Bayes analysis of the same data and with a Bayesian analysis based on an alternative commonly used prior.
A URI 4-NODE QUADRILATERAL ELEMENT BY ASSUMED STRAIN METHOD FOR NONLINEAR PROBLEMS
Institute of Scientific and Technical Information of China (English)
WANG Jinyan; CHEN Jun; LI Minghui
2004-01-01
In this paper one-point quadrature "assumed strain" mixed element formulation based on the Hu-Washizu variational principle is presented. Special care is taken to avoid hourglass modes and volumetric locking as well as shear locking. The assumed strain fields are constructed so that those portions of the fields which lead to volumetric and shear locking phenomena are eliminated by projection, while the implementation of the proposed URI scheme is straightforward to suppress hourglass modes. In order to treat geometric nonlinearities simply and efficiently, a corotational coordinate system is used. Several numerical examples are given to demonstrate the performance of the suggested formulation, including nonlinear static/dynamic mechanical problems.
Local-instantaneous filtering in the integral transform solution of nonlinear diffusion problems
Macêdo, E. N.; Cotta, R. M.; Orlande, H. R. B.
A novel filtering strategy is proposed to be utilized in conjunction with the Generalized Integral Transform Technique (GITT), in the solution of nonlinear diffusion problems. The aim is to optimize convergence enhancement, yielding computationally efficient eigenfunction expansions. The proposed filters include space and time dependence, extracted from linearized versions of the original partial differential system. The scheme automatically updates the filter along the time integration march, as the required truncation orders for the user requested accuracy begin to exceed a prescribed maximum system size. A fully nonlinear heat conduction example is selected to illustrate the computational performance of the filtering strategy, against the classical single-filter solution behavior.
Solution of transient optimization problems by using an algorithm based on nonlinear programming
Teren, F.
1977-01-01
A new algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
Nonlinear evolution equations associated with the chiral-field spectral problem
Energy Technology Data Exchange (ETDEWEB)
Bruschi, M.; Ragnisco, O. (Istituto Nazionale di Fisica Nucleare, Roma (Italy); Dipt. di Fisica, Univ. Rome (Italy))
1985-08-11
In this paper we derive and investigate the class of nonlinear evolution equations (NEEs) associated with the linear problem psisub(x) = lambdaApsi. It turns out that many physically interesting NEEs pertain to this class: for instance, the chiral-field equation, the nonlinear Klein-Gordon equations, the Heisenberg and Papanicolau spin chain models, the modified Boussinesq equation, the Wadati-Konno-Ichikawa equations, etc. We display also the Baecklund transformations for such a class and exploit them to derive in a special case the one-soliton solution.
An iterative regularization method for nonlinear problems based on Bregman projections
Maaß, Peter; Strehlow, Robin
2016-11-01
In this paper, we present an iterative method for the regularization of ill-posed, nonlinear problems. The approach is based on the Bregman projection onto stripes the width of which is controlled by both the noise level and the structure of the operator. In our investigations, we follow (Lorenz et al 2014 SIAM J. Imaging Sci. 7 1237-62) and extend the respective method to the setting of nonlinear operators. Furthermore, we present a proof for the regularizing properties of the method.
On the Cauchy problem for nonlinear Schrödinger equations with rotation
Antonelli, Paolo
2011-10-01
We consider the Cauchy problem for (energy-subcritical) nonlinear Schrödinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for superuid quantum gases in rotating traps. We prove global existence (in the energy space) for defocusing nonlinearities without any restriction on the rotation frequency, generalizing earlier results given in [11, 12]. Moreover, we find that the rotation term has a considerable in fiuence in proving finite time blow-up in the focusing case.
The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation
Directory of Open Access Journals (Sweden)
Bergfinnur Durhuus
2010-06-01
Full Text Available We investigate scattering properties of a Moyal deformed version of the nonlinear Schrödinger equation in an even number of space dimensions. With rather weak conditions on the degree of nonlinearity, the Cauchy problem for general initial data has a unique globally defined solution, and also has solitary wave solutions if the interaction potential is suitably chosen. We demonstrate how to set up a scattering framework for equations of this type, including appropriate decay estimates of the free time evolution and the construction of wave operators defined for small scattering data in the general case and for arbitrary scattering data in the rotationally symmetric case.
Solution of transient optimization problems by using an algorithm based on nonlinear programming
Teren, F.
1977-01-01
A new algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
Domain decomposition based iterative methods for nonlinear elliptic finite element problems
Energy Technology Data Exchange (ETDEWEB)
Cai, X.C. [Univ. of Colorado, Boulder, CO (United States)
1994-12-31
The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.
Energy Technology Data Exchange (ETDEWEB)
Kim, D.; Ghanem, R. [State Univ. of New York, Buffalo, NY (United States)
1994-12-31
Multigrid solution technique to solve a material nonlinear problem in a visual programming environment using the finite element method is discussed. The nonlinear equation of equilibrium is linearized to incremental form using Newton-Rapson technique, then multigrid solution technique is used to solve linear equations at each Newton-Rapson step. In the process, adaptive mesh refinement, which is based on the bisection of a pair of triangles, is used to form grid hierarchy for multigrid iteration. The solution process is implemented in a visual programming environment with distributed computing capability, which enables more intuitive understanding of solution process, and more effective use of resources.
Institute of Scientific and Technical Information of China (English)
Shuang Ping TAO; Shang Bin CUI
2005-01-01
This paper is devoted to studying the initial value problem of the modified nonlinear Kawahara equation ()u/()t+ a u2()u/()m + β()3u/()x3 + γ()5u-()x5 = 0, (x, t) ∈ We first establish several Strichartz type estimates for the fundamental solution of the corresponding linear problem. Then we apply such estimates to prove local and global existence of solutions for the initial value problem of the modified nonlinear Karahara equation. The results show that a local solution exists if the initial function u0(x) ∈ Hs(R) with s ≥ 1/4, and a global solution exists if s ≥ 2.
A LQP BASED INTERIOR PREDICTION-CORRECTION METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS
Institute of Scientific and Technical Information of China (English)
Bing-sheng He; Li-zhi Liao; Xiao-ming Yuan
2006-01-01
To solve nonlinear complementarity problems (NCP), at each iteration, the classical proximal point algorithm solves a well-conditioned sub-NCP while the LogarithmicQuadratic Proximal (LQP) method solves a system of nonlinear equations (LQP system). This paper presents a practical LQP method-based prediction-correction method for NCP.The predictor is obtained via solving the LQP system approximately under significantly relaxed restriction, and the new iterate (the corrector) is computed directly by an explicit formula derived from the original LQP method. The implementations are very easy to be carried out. Global convergence of the method is proved under the same mild assumptions as the original LQP method. Finally, numerical results for traffic equilibrium problems are provided to verify that the method is effective for some practical problems.
Murphy, Patrick Charles
1985-01-01
An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.
Product of Toeplitz Operators on the Harmonic Dirichlet Space
Institute of Scientific and Technical Information of China (English)
Lian Kuo ZHAO
2012-01-01
In this paper,we study Toeplitz operators with harmonic symbols on the harmonic Dirichlet space,and show that the product of two Toeplitz operators is another Toeplitz operator only if one factor is constant.
Quantum “violation” of Dirichlet boundary condition
Directory of Open Access Journals (Sweden)
I.Y. Park
2017-02-01
Full Text Available Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a tension between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum-corrected black hole solution of the 1PI action no longer obeys, in the naive manner one may expect, the Dirichlet boundary conditions imposed at the classical level. We attribute the ‘violation’ of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.
A GLOBALLY DERIVATIVE-FREE DESCENT METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS
Institute of Scientific and Technical Information of China (English)
Hou-duo Qi; Yu-zhong Zhang
2000-01-01
Based on a class of functions. which generalize the squared Fischer-Burmeister NCP function and have many desirable properties as the latter function has, we reformulate nonlinear complementarity problem (NCP for short) as an equivalent unconstrained optimization problem, for which we propose a derivative-free descent method in monotone case. We show its global convergence under some mild conditions. If F, the function involved in NCP, is Ro－function, the optimization problem has bounded level sets. A local property of the merit function is discussed. Finally, we report some numerical results.
Institute of Scientific and Technical Information of China (English)
Qin Ni
2001-01-01
An NGTN method was proposed for solving large-scale sparse nonlinear programming (NLP) problems. This is a hybrid method of a truncated Newton direction and a modified negative gradient direction, which is suitable for handling sparse data structure and possesses Q-quadratic convergence rate. The global convergence of this new method is proved,the convergence rate is further analysed, and the detailed implementation is discussed in this paper. Some numerical tests for solving truss optimization and large sparse problems are reported. The theoretical and numerical results show that the new method is efficient for solving large-scale sparse NLP problems.
Rezaee, Hamed; Abdollahi, Farzaneh
2016-12-06
The leaderless consensus problem over a class of high-order nonlinear multiagent systems (MASs) is studied. A robust protocol is proposed which guarantees achieving consensus in the network in the presences of uncertainties in agents models. Achieving consensus in the case of stochastic links failure is studied as well. Based on the concept super-martingales, it is shown that if the probability of the network connectivity is not zero, under some conditions, achieving almost sure consensus in the network can be guaranteed. Despite existing consensus protocols for high-order stochastic networks, the proposed consensus protocol in this paper is robust to uncertain nonlinearities in the agents models, and it can be designed independent of knowledge on the set of feasible topologies (topologies with nonzero probabilities). Numerical examples for a team of single-link flexible joint manipulators with fourth-order models verify the accuracy of the proposed strategy for consensus control of high-order MASs with uncertain nonlinearities.
An iterative HAM approach for nonlinear boundary value problems in a semi-infinite domain
Zhao, Yinlong; Lin, Zhiliang; Liao, Shijun
2013-09-01
In this paper, we propose an iterative approach to increase the computation efficiency of the homotopy analysis method (HAM), a analytic technique for highly nonlinear problems. By means of the Schmidt-Gram process (Arfken et al., 1985) [15], we approximate the right-hand side terms of high-order linear sub-equations by a finite set of orthonormal bases. Based on this truncation technique, we introduce the Mth-order iterative HAM by using each Mth-order approximation as a new initial guess. It is found that the iterative HAM is much more efficient than the standard HAM without truncation, as illustrated by three nonlinear differential equations defined in an infinite domain as examples. This work might greatly improve the computational efficiency of the HAM and also the Mathematica package BVPh for nonlinear BVPs.
Directory of Open Access Journals (Sweden)
Sie Long Kek
2015-01-01
Full Text Available A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.
EXACT AUGMENTED LAGRANGIAN FUNCTION FOR NONLINEAR PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS
Institute of Scientific and Technical Information of China (English)
DU Xue-wu; ZHANG Lian-sheng; SHANG You-lin; LI Ming-ming
2005-01-01
An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions,the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, from the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented.
Variational ansatz for the nonlinear Landau-Zener problem for cold atom association
Energy Technology Data Exchange (ETDEWEB)
Ishkhanyan, A [Institute for Physical Research NAS of Armenia, 0203 Ashtarak-2 (Armenia); Joulakian, B [LPMC, Universite Paul Verlaine-Metz, 1 Bld Arago, 57078 Metz Cedex 3 (France); Suominen, K-A [Department of Physics and Astronomy, University of Turku, 20014 Turun yliopisto (Finland)
2009-11-28
We present a rigorous analysis of the Landau-Zener linear-in-time term crossing problem for quadratic-nonlinear systems relevant to the coherent association of ultracold atoms in degenerate quantum gases. Our treatment is based on an exact third-order nonlinear differential equation for the molecular state probability. Applying a variational two-term ansatz, we construct a simple approximation that accurately describes the whole-time dynamics of the coupled atom-molecular system for any set of involved parameters. Ensuring an absolute error of less than 10{sup -5} for the final transition probability, the resultant solution improves by several orders of magnitude the accuracy of the previous approximations by A Ishkhanyan et al developed separately for the weak coupling (2005 J. Phys. A: Math. Gen. 38 3505) and strong interaction (2006 J. Phys. A: Math. Gen. 39 14887) limits. In addition, the constructed approximation covers the whole moderate-coupling regime, providing this intermediate regime with the same accuracy as the two mentioned limits. The obtained results reveal the remarkable observation, that for the strong-coupling limit the resonance crossing is mostly governed by the nonlinearity, while the coherent atom-molecular oscillations arising soon after the resonance has been crossed are basically of a linear nature. This observation is supposed to be of a general character, due to the basic attributes of the resonance-crossing processes in the nonlinear quantum systems of the discussed type of involved quadratic nonlinearity. (fast track communication)
Nonlinear quantum mechanics, the superposition principle, and the quantum measurement problem
Indian Academy of Sciences (India)
Kinjalk Lochan; T P Singh
2011-01-01
There are four reasons why our present knowledge and understanding of quantum mechanics can be regarded as incomplete. (1) The principle of linear superposition has not been experimentally tested for position eigenstates of objects having more than about a thousand atoms. (2) There is no universally agreed upon explanation for the process of quantum measurement. (3) There is no universally agreed upon explanation for the observed fact that macroscopic objects are not found in superposition of position eigenstates. (4) Most importantly, the concept of time is classical and hence external to quantum mechanics: there should exist an equivalent reformulation of the theory which does not refer to an external classical time. In this paper we argue that such a reformulation is the limiting case of a nonlinear quantum theory, with the nonlinearity becoming important at the Planck mass scale. Such a nonlinearity can provide insights into the aforesaid problems. We use a physically motivated model for a nonlinear Schr ¨odinger equation to show that nonlinearity can help in understanding quantum measurement. We also show that while the principle of linear superposition holds to a very high accuracy for atomic systems, the lifetime of a quantum superposition becomes progressively smaller, as one goes from microscopic to macroscopic objects. This can explain the observed absence of position superpositions in macroscopic objects (lifetime is too small). It also suggests that ongoing laboratory experiments may be able to detect the ﬁnite superposition lifetime for mesoscopic objects in the near future.
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-05-01
An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.
Prior Design for Dependent Dirichlet Processes: An Application to Marathon Modeling.
Directory of Open Access Journals (Sweden)
Melanie F Pradier
Full Text Available This paper presents a novel application of Bayesian nonparametrics (BNP for marathon data modeling. We make use of two well-known BNP priors, the single-p dependent Dirichlet process and the hierarchical Dirichlet process, in order to address two different problems. First, we study the impact of age, gender and environment on the runners' performance. We derive a fair grading method that allows direct comparison of runners regardless of their age and gender. Unlike current grading systems, our approach is based not only on top world records, but on the performances of all runners. The presented methodology for comparison of densities can be adopted in many other applications straightforwardly, providing an interesting perspective to build dependent Dirichlet processes. Second, we analyze the running patterns of the marathoners in time, obtaining information that can be valuable for training purposes. We also show that these running patterns can be used to predict finishing time given intermediate interval measurements. We apply our models to New York City, Boston and London marathons.
Ghattassi, Mohamed; Roche, Jean Rodolphe; Schmitt, Didier; Boutayeb, Mohamed
2016-01-01
This paper deals with local existence and uniqueness results for a transient two-dimensional combined nonlinear radiative-conductive system. This system describes the heat transfer for a grey, semi-transparent and non-scattering medium with homogeneous Dirichlet boundary conditions. We reformulate the full transient state system as a fixed-point problem. The existence and uniqueness proof rests upon the Banach fixed-point Theorem assuming the initial data T 0 is non-negative and sufficiently ...
Predicting Component Failures Using Latent Dirichlet Allocation
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Hailin Liu
2015-01-01
Full Text Available Latent Dirichlet Allocation (LDA is a statistical topic model that has been widely used to abstract semantic information from software source code. Failure refers to an observable error in the program behavior. This work investigates whether semantic information and failures recorded in the history can be used to predict component failures. We use LDA to abstract topics from source code and a new metric (topic failure density is proposed by mapping failures to these topics. Exploring the basic information of topics from neighboring versions of a system, we obtain a similarity matrix. Multiply the Topic Failure Density (TFD by the similarity matrix to get the TFD of the next version. The prediction results achieve an average 77.8% agreement with the real failures by considering the top 3 and last 3 components descending ordered by the number of failures. We use the Spearman coefficient to measure the statistical correlation between the actual and estimated failure rate. The validation results range from 0.5342 to 0.8337 which beats the similar method. It suggests that our predictor based on similarity of topics does a fine job of component failure prediction.
Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics
DEFF Research Database (Denmark)
Iwankiewicz, R.; Nielsen, Søren R. K.
-numerical techniques suitable for Markov response problems such as moments equation, Petrov-Galerkin and cell-to-cell mapping techniques are briefly discussed. Usefulness of these techniques is limited by the fact that effectiveness of each of them depends on the mean rate of impulses. Another limitation is the size...... of the problem, i.e. the number of state variables of the dynamical systems. In contrast, the application of the simulation techniques is not limited to Markov problems, nor is it dependent on the mean rate of impulses. Moreover their use is straightforward for a large class of point processes, at least......Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically...
Tamma, Kumar K.; Railkar, Sudhir B.
1988-01-01
The present paper describes the applicability of hybrid transfinite element modeling/analysis formulations for nonlinear heat conduction problems involving phase change. The methodology is based on application of transform approaches and classical Galerkin schemes with finite element formulations to maintain the modeling versatility and numerical features for computational analysis. In addition, in conjunction with the above, the effects due to latent heat are modeled using enthalpy formulations to enable a physically realistic approximation to be dealt computationally for materials exhibiting phase change within a narrow band of temperatures. Pertinent details of the approach and computational scheme adapted are described in technical detail. Numerical test cases of comparative nature are presented to demonstrate the applicability of the proposed formulations for numerical modeling/analysis of nonlinear heat conduction problems involving phase change.
Energy Technology Data Exchange (ETDEWEB)
Lin Jaeyuh [Chang Jung Univ., Tainan (Taiwan, Province of China); Chen Hantaw [National Cheng Kung Univ., Tainan (Taiwan, Province of China). Dept. of Mechanical Engineering
1997-09-01
A hybrid numerical scheme combining the Laplace transform and control-volume methods is presented to solve nonlinear two-dimensional phase-change problems with the irregular geometry. The Laplace transform method is applied to deal with the time domain, and then the control-volume method is used to discretize the transformed system in the space domain. Nonlinear terms induced by the temperature-dependent thermal properties are linearized by using the Taylor series approximation. Control-volume meshes in the solid and liquid regions during simulations are generated by using the discrete transfinite mapping method. The location of the phase-change interface and the isothermal distributions are determined. Comparison of these results with previous results shows that the present numerical scheme has good accuracy for two-dimensional phase-change problems. (orig.). With 10 figs.
Homotopy deform method for reproducing kernel space for nonlinear boundary value problems
Indian Academy of Sciences (India)
MIN-QIANG XU; YING-ZHEN LIN
2016-10-01
In this paper, the combination of homotopy deform method (HDM) and simplified reproducing kernel method (SRKM) is introduced for solving the boundary value problems (BVPs) of nonlinear differential equations. The solution methodology is based on Adomian decomposition and reproducing kernel method (RKM). By the HDM, the nonlinear equations can be converted into a series of linear BVPs. After that, the simplified reproducing kernel method, which not only facilitates the reproducing kernel but also avoids the time-consuming Schmidt orthogonalization process, is proposed to solve linear equations. Some numerical test problems including ordinary differential equations and partial differential equations are analysed to illustrate the procedure and confirm the performance of the proposed method. The results faithfully reveal that our algorithm is considerably accurate and effective as expected.
Numerical solution of a nonlinear least squares problem in digital breast tomosynthesis
Landi, G.; Loli Piccolomini, E.; Nagy, J. G.
2015-11-01
In digital tomosynthesis imaging, multiple projections of an object are obtained along a small range of different incident angles in order to reconstruct a pseudo-3D representation (i.e., a set of 2D slices) of the object. In this paper we describe some mathematical models for polyenergetic digital breast tomosynthesis image reconstruction that explicitly takes into account various materials composing the object and the polyenergetic nature of the x-ray beam. A polyenergetic model helps to reduce beam hardening artifacts, but the disadvantage is that it requires solving a large-scale nonlinear ill-posed inverse problem. We formulate the image reconstruction process (i.e., the method to solve the ill-posed inverse problem) in a nonlinear least squares framework, and use a Levenberg-Marquardt scheme to solve it. Some implementation details are discussed, and numerical experiments are provided to illustrate the performance of the methods.
Baum, J. D.; Levine, J. N.
1980-01-01
The selection of a satisfactory numerical method for calculating the propagation of steep fronted shock life waveforms in a solid rocket motor combustion chamber is discussed. A number of different numerical schemes were evaluated by comparing the results obtained for three problems: the shock tube problems; the linear wave equation, and nonlinear wave propagation in a closed tube. The most promising method--a combination of the Lax-Wendroff, Hybrid and Artificial Compression techniques, was incorporated into an existing nonlinear instability program. The capability of the modified program to treat steep fronted wave instabilities in low smoke tactical motors was verified by solving a number of motor test cases with disturbance amplitudes as high as 80% of the mean pressure.
A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems
Directory of Open Access Journals (Sweden)
S. S. Motsa
2013-01-01
Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.
Directory of Open Access Journals (Sweden)
Morteza Ebrahimi
2012-01-01
Full Text Available The purpose of the present study is to provide a fast and accurate algorithm for identifying the medium temperature and the unknown radiation term from an overspecified condition on the boundary in an inverse problem of linear heat equation with nonlinear boundary condition. The design of the paper is to employ Taylor’s series expansion for linearize nonlinear term and then finite-difference approximation to discretize the problem domain. Owing to the application of the finite difference scheme, a large sparse system of linear algebraic equations is obtained. An approach of Monte Carlo method is employed to solve the linear system and estimate unknown radiation term. The Monte Carlo optimization is adopted to modify the estimated values. Results show that a good estimation on the radiation term can be obtained within a couple of minutes CPU time at pentium IV-2.4 GHz PC.
Murio, Diego A.
1991-01-01
An explicit and unconditionally stable finite difference method for the solution of the transient inverse heat conduction problem in a semi-infinite or finite slab mediums subject to nonlinear radiation boundary conditions is presented. After measuring two interior temperature histories, the mollification method is used to determine the surface transient heat source if the energy radiation law is known. Alternatively, if the active surface is heated by a source at a rate proportional to a given function, the nonlinear surface radiation law is then recovered as a function of the interface temperature when the problem is feasible. Two typical examples corresponding to Newton cooling law and Stefan-Boltzmann radiation law respectively are illustrated. In all cases, the method predicts the surface conditions with an accuracy suitable for many practical purposes.
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MOHAMED KEZZAR
2015-08-01
Full Text Available In this research, an efficient technique of computation considered as a modified decomposition method was proposed and then successfully applied for solving the nonlinear problem of the two dimensional flow of an incompressible viscous fluid between nonparallel plane walls. In fact this method gives the nonlinear term Nu and the solution of the studied problem as a power series. The proposed iterative procedure gives on the one hand a computationally efficient formulation with an acceleration of convergence rate and on the other hand finds the solution without any discretization, linearization or restrictive assumptions. The comparison of our results with those of numerical treatment and other earlier works shows clearly the higher accuracy and efficiency of the used Modified Decomposition Method.
Solution of the nonlinear inverse scattering problem by T -matrix completion. II. Simulations
Levinson, Howard W.; Markel, Vadim A.
2016-10-01
This is Part II of the paper series on data-compatible T -matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043317 (2016), 10.1103/PhysRevE.94.043317] contains theory and here we present simulations for inverse scattering of scalar waves. The underlying mathematical model is the scalar wave equation and the object function that is reconstructed is the medium susceptibility. The simulations are relevant to ultrasound tomographic imaging and seismic tomography. It is shown that DCTMC is a viable method for solving strongly nonlinear inverse problems with large data sets. It provides not only the overall shape of the object, but the quantitative contrast, which can correspond, for instance, to the variable speed of sound in the imaged medium.
ON TRANSMISSION PROBLEM FOR VISCOELASTIC WAVE EQUATION WITH A LOCALIZED A NONLINEAR DISSIPATION
Institute of Scientific and Technical Information of China (English)
Jeong Ja BAE; Seong Sik KIM
2013-01-01
In this article,we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physically different types of materials,one component being a Kirchhoff type wave equation with time dependent localized dissipation which is effective only on a neighborhood of certain part of boundary,while the other being a Kirchhoff type viscoelastic wave equation with nonlinear memory.
EXISTENCE OF SOLUTIONS OF A FAMILY OF NONLINEAR BOUNDARY VALUE PROBLEMS IN L2-SPACES
Institute of Scientific and Technical Information of China (English)
WeiLi; ZhouHaiyun
2005-01-01
By using the perturbation results of sums of ranges of accretive mappings of Calvert and Gupta (1978),the abstract results on the existence of solutions of a family of nonlinear boundary value problems in L2 (Ω) are studied. The equation discussed in this paper and the methods used here are extension and complement to the corresponding results of Wei Li and He Zhen's previous papers. Especially,some new techniques are used in this paper.
Analytical Approximation Method for the Center Manifold in the Nonlinear Output Regulation Problem
Suzuki, Hidetoshi; Sakamoto, Noboru; Celikovský, Sergej
In nonlinear output regulation problems, it is necessary to solve the so-called regulator equations consisting of a partial differential equation and an algebraic equation. It is known that, for the hyperbolic zero dynamics case, solving the regulator equations is equivalent to calculating a center manifold for zero dynamics of the system. The present paper proposes a successive approximation method for obtaining center manifolds and shows its effectiveness by applying it for an inverted pendulum example.
C-L METHOD AND ITS APPLICATION TO ENGINEERING NONLINEAR DYNAMICAL PROBLEMS
Institute of Scientific and Technical Information of China (English)
陈予恕; 丁千
2001-01-01
The C-L method was generalized from Liapunov-Schmidt reduction method,combined with theory of singularities, for study of non-autonomous dynamical systems to obtain the typical bifurcating response curves in the system parameter spaces. This method has been used , as an example, to analyze the engineering nonlinear dynamical problems by obtaining the bifurcation programs and response curves which are useful in developing tech niques of control to subharmonic instability of large rotating machinery.
Numerical method for nonlinear two-phase displacement problem and its application
Institute of Scientific and Technical Information of China (English)
YUAN Yi-rang; LIANG Dong; RUI Hong-xing; DU Ning; WANG Wen-qia
2008-01-01
For the three-dimensional nonlinear two-phase displacement problem, the modified upwind finite difference fractional steps schemes were put forward. Some techniques, such as calculus of variations, induction hypothesis, decomposition of high order difference operators, the theory of prior estimates and techniques were used. Optimal order estimates were derived for the error in the approximation solution. These methods have been successfully used to predict the consequences of seawater intrusion and protection projects.
Solvability of a three-point nonlinear boundary-value problem
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Assia Guezane-Lakoud
2010-09-01
Full Text Available Using the Leray Schauder nonlinear alternative, we prove the existence of a nontrivial solution for the three-point boundary-value problem $$displaylines{ u''+f(t,u= 0,quad 0
Positive solutions for a nonlinear periodic boundary-value problem with a parameter
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Jingliang Qiu
2012-08-01
Full Text Available Using topological degree theory with a partially ordered structure of space, sufficient conditions for the existence and multiplicity of positive solutions for a second-order nonlinear periodic boundary-value problem are established. Inspired by ideas in Guo and Lakshmikantham [6], we study the dependence of positive periodic solutions as a parameter approaches infinity, $$ lim_{lambdao +infty}|x_{lambda}|=+infty,quadhbox{or}quad lim_{lambdao+infty}|x_{lambda}|=0. $$
A New Subspace Correction Method for Nonlinear Unconstrained Convex Optimization Problems
Institute of Scientific and Technical Information of China (English)
Rong-liang CHEN; Jin-ping ZENG
2012-01-01
This paper gives a new subspace correction algorithm for nonlinear unconstrained convex optimization problems based on the multigrid approach proposed by S.Nash in 2000 and the subspace correction algorithm proposed by X.Tai and J.Xu in 2001.Under some reasonable assumptions,we obtain the convergence as well as a convergence rate estimate for the algorithm.Numerical results show that the algorithm is effective.
Validation of Finite Element Solutions of Nonlinear, Periodic Eddy Current Problems
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Plasser René
2014-12-01
Full Text Available An industrial application is presented to validate a finite element analysis of 3-dimensional, nonlinear eddy-current problems with periodic excitation. The harmonic- balance method and the fixed-point technique are applied to get the steady state solution using the finite element method. The losses occurring in steel reinforcements underneath a reactor due to induced eddy-currents are computed and compared to measurements.
Flying randomly in $\\mathbb{R}^d$ with Dirichlet displacements
De Gregorio, Alessandro
2011-01-01
Random flights in $\\mathbb{R}^d,d\\geq 2,$ with Dirichlet-distributed displacements and uniformly distributed orientation are analyzed. The explicit characteristic functions of the position $\\underline{\\bf X}_d(t),\\,t>0,$ when the number of changes of direction is fixed are obtained. The probability distributions are derived by inverting the characteristic functions for all dimensions $d$ of $\\mathbb{R}^d$ and many properties of the probabilistic structure of $\\underline{\\bf X}_d(t),t>0,$ are examined. If the number of changes of direction is randomized by means of a fractional Poisson process, we are able to obtain explicit distributions for $P\\{\\underline{\\bf X}_d(t)\\in d\\underline{\\bf x}_d\\}$ for all $d\\geq 2$. A Section is devoted to random flights in $\\mathbb{R}^3$ where the general results are discussed. The existing literature is compared with the results of this paper where in our view the classical Pearson's problem of random flights is resolved by suitably randomizing the step lengths. The random fli...
Morozov-type discrepancy principle for nonlinear ill-posed problems under -condition
Indian Academy of Sciences (India)
M Thamban Nair
2015-05-01
For proving the existence of a regularization parameter under a Morozov-type discrepancy principle for Tikhonov regularization of nonlinear ill-posed problems, it is required to impose additional nonlinearity assumptions on the forward operator. Lipschitz continuity of the Freéchet derivative and requirement of the Lipschitz constant to depend on a source condition is one such restriction (Ramlau P, Numer. Funct. Anal. Optim. 23(1&22) (2003) 147–172). Another nonlinearity condition considered by Scherzer (Computing, 51 (1993) 45–60) was by requiring the forward operator to be close to a linear operator in a restricted sense. A seemingly natural nonlinear assumption which appears in many applications which attracted attention in various contexts of the study of nonlinear problems is the so-called -condition. However, a Morozov-type discrepancy principle together with -condition does not seem to have been studied, except in a recent paper by the author (Bull. Aust. Math. Soc. 79 (2009) 337–342), where error estimates under a general source condition is derived, by assuming the existence of the parameter. In this paper, the existence of the parameter satisfying a Morozov-type discrepancy principle is proved under the -condition on the forward operator, by assuming the source condition as in the papers of Scherzer (Computing, 51 (1993) 45–60) and Ramlau (Numer. Funct. Anal. Optim. 23(1&22) (2003) 147–172). This source condition is, in fact, a special case of the source condition in the author’s paper (Bull. Aust. Math. Soc. 79 (2009) 337–342).
A finite element algorithm for high-lying eigenvalues with Neumann and Dirichlet boundary conditions
Báez, G.; Méndez-Sánchez, R. A.; Leyvraz, F.; Seligman, T. H.
2014-01-01
We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions, or combinations of either for different parts of the boundary. We use an inverse power plus Gauss-Seidel algorithm to solve the generalized eigenvalue problem. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We checked the algorithm by comparing the cumulative level density of the spectrum obtained numerically with the theoretical prediction given by the Weyl formula. We found a systematic deviation due to the discretization, not to the algorithm itself.
The viscous surface-internal wave problem: nonlinear Rayleigh-Taylor instability
Wang, Yanjin
2011-01-01
We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom in a three-dimensional horizontally periodic setting. The effect of surface tension is either taken into account at both free boundaries or neglected at both. We are concerned with the Rayleigh-Taylor instability, so we assume that the upper fluid is heavier than the lower fluid. When the surface tension at the free internal interface is below a critical value, which we identify, we establish that the problem under consideration is nonlinearly unstable.
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Ying Wang
2015-03-01
Full Text Available In this article, we study the existence of multiple positive solutions for singular semipositone boundary-value problem (BVP with integral boundary conditions on infinite intervals. By using the properties of the Green's function and the Guo-Krasnosel'skii fixed point theorem, we obtain the existence of multiple positive solutions under conditions concerning the nonlinear functions. The method in this article can be used for a large number of problems. We illustrate the validity of our results with an example in the last section.
POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
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FAOUZI HADDOUCHI
2015-11-01
Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.
Verified solutions of two-point boundary value problems for nonlinear oscillators
Bünger, Florian
Using techniques introduced by Nakao [4], Oishi [5, 6] and applied by Takayasu, Oishi, Kubo [11, 12] to certain nonlinear two-point boundary value problems (see also Rump [7], Chapter 15), we provide a numerical method for verifying the existence of weak solutions of two-point boundary value problems of the form -u″ = a(x, u) + b(x, u)u‧, 0 b are functions that fulfill some regularity properties. The numerical approximation is done by cubic spline interpolation. Finally, the method is applied to the Duffing, the van der Pol and the Toda oscillator. The rigorous numerical computations were done with INTLAB [8].
Nonlinear systems of differential inequalities and solvability of certain boundary value problems
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Tvrdý Milan
2001-01-01
Full Text Available In the paper we present some new existence results for nonlinear second order generalized periodic boundary value problems of the form These results are based on the method of lower and upper functions defined as solutions of the system of differential inequalities associated with the problem and their relation to the Leray–Schauder topological degree of the corresponding operator. Our main goal consists in a fairly general definition of these functions as couples from . Some conditions ensuring their existence are indicated, as well.
A mixed Newton-Tikhonov method for nonlinear ill-posed problems
Institute of Scientific and Technical Information of China (English)
Chuan-gang KANG; Guo-qiang HE
2009-01-01
Newton type methods are one kind of the efficient methods to solve nonlinear ill-posed problems,which have attracted extensive attention.However,computational cost of Newton type methods is high because practical problems are complicated.We propose a mixed Newton-Tikhonov method,i.e.,one step Newton-Tikhonov method with several other steps of simplified Newton-Tikhonov method.Convergence and stability of this method are proved under some conditions.Numerical experiments show that the proposed method has obvious advantages over the classical Newton method in terms of computational costs.
An NE/SQP method for the bounded nonlinear complementarity problem
Energy Technology Data Exchange (ETDEWEB)
Gabriel, S.A. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.
1995-05-30
NE/SQP is a recent algorithm that has proven quite effective for solving the pure and mixed forms of the nonlinear complementarity problem (NCP). NE/SQP is robust in the sense that its direction-finding subproblems are always solvable; in addition, the convergence rate of this method is Q-quadratic. In this paper the author considers a generalized version of NE/SQP proposed by Pang and Qi, that is suitable for the bounded NCP. The author extends their work by demonstrating a stronger convergence result and then tests a proposed method on several numerical problems.
Sakhnovich, Lev A; Roitberg, Inna Ya
2013-01-01
This monograph fits theclearlyneed for books with a rigorous treatment of theinverse problems for non-classical systems and that of initial-boundary-value problems for integrable nonlinear equations. The authorsdevelop a unified treatment of explicit and global solutions via the transfer matrix function in a form due to Lev A. Sakhnovich. The book primarily addresses specialists in the field. However, it is self-contained andstarts with preliminaries and examples, and hencealso serves as an introduction for advanced graduate students in the field.
Improved simple optimization (SOPT algorithm for unconstrained non-linear optimization problems
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J. Thomas
2016-09-01
Full Text Available In the recent years, population based meta-heuristic are developed to solve non-linear optimization problems. These problems are difficult to solve using traditional methods. Simple optimization (SOPT algorithm is one of the simple and efficient meta-heuristic techniques to solve the non-linear optimization problems. In this paper, SOPT is compared with some of the well-known meta-heuristic techniques viz. Artificial Bee Colony algorithm (ABC, Particle Swarm Optimization (PSO, Genetic Algorithm (GA and Differential Evolutions (DE. For comparison, SOPT algorithm is coded in MATLAB and 25 standard test functions for unconstrained optimization having different characteristics are run for 30 times each. The results of experiments are compared with previously reported results of other algorithms. Promising and comparable results are obtained for most of the test problems. To improve the performance of SOPT, an improvement in the algorithm is proposed which helps it to come out of local optima when algorithm gets trapped in it. In almost all the test problems, improved SOPT is able to get the actual solution at least once in 30 runs.
A high performance neural network for solving nonlinear programming problems with hybrid constraints
Tao, Qing; Cao, Jinde; Xue, Meisheng; Qiao, Hong
2001-09-01
A continuous neural network is proposed in this Letter for solving optimization problems. It not only can solve nonlinear programming problems with the constraints of equality and inequality, but also has a higher performance. The main advantage of the network is that it is an extension of Newton's gradient method for constrained problems, the dynamic behavior of the network under special constraints and the convergence rate can be investigated. Furthermore, the proposed network is simpler than the existing networks even for solving positive definite quadratic programming problems. The network considered is constrained by a projection operator on a convex set. The advanced performance of the proposed network is demonstrated by means of simulation of several numerical examples.
A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise
Clason, Christian
2012-01-01
This work is concerned with nonlinear parameter identification in partial differential equations subject to impulsive noise. To cope with the non-Gaussian nature of the noise, we consider a model with L 1 fitting. However, the nonsmoothness of the problem makes its efficient numerical solution challenging. By approximating this problem using a family of smoothed functionals, a semismooth Newton method becomes applicable. In particular, its superlinear convergence is proved under a second-order condition. The convergence of the solution to the approximating problem as the smoothing parameter goes to zero is shown. A strategy for adaptively selecting the regularization parameter based on a balancing principle is suggested. The efficiency of the method is illustrated on several benchmark inverse problems of recovering coefficients in elliptic differential equations, for which one- and two-dimensional numerical examples are presented. © by SIAM.
Luo, Xiaodong
2014-10-01
The ensemble Kalman filter (EnKF) is an efficient algorithm for many data assimilation problems. In certain circumstances, however, divergence of the EnKF might be spotted. In previous studies, the authors proposed an observation-space-based strategy, called residual nudging, to improve the stability of the EnKF when dealing with linear observation operators. The main idea behind residual nudging is to monitor and, if necessary, adjust the distances (misfits) between the real observations and the simulated ones of the state estimates, in the hope that by doing so one may be able to obtain better estimation accuracy. In the present study, residual nudging is extended and modified in order to handle nonlinear observation operators. Such extension and modification result in an iterative filtering framework that, under suitable conditions, is able to achieve the objective of residual nudging for data assimilation problems with nonlinear observation operators. The 40-dimensional Lorenz-96 model is used to illustrate the performance of the iterative filter. Numerical results show that, while a normal EnKF may diverge with nonlinear observation operators, the proposed iterative filter remains stable and leads to reasonable estimation accuracy under various experimental settings.
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
The iterative technique of sign-changing solution is studied for a nonlinear third-order two-point boundary value problem, where the nonlinear term has the time sin-gularity. By applying the monotonically iterative technique, an existence theorem is established and two useful iterative schemes are obtained.
On large-scale nonlinear programming techniques for solving optimal control problems
Energy Technology Data Exchange (ETDEWEB)
Faco, J.L.D.
1994-12-31
The formulation of decision problems by Optimal Control Theory allows the consideration of their dynamic structure and parameters estimation. This paper deals with techniques for choosing directions in the iterative solution of discrete-time optimal control problems. A unified formulation incorporates nonlinear performance criteria and dynamic equations, time delays, bounded state and control variables, free planning horizon and variable initial state vector. In general they are characterized by a large number of variables, mostly when arising from discretization of continuous-time optimal control or calculus of variations problems. In a GRG context the staircase structure of the jacobian matrix of the dynamic equations is exploited in the choice of basic and super basic variables and when changes of basis occur along the process. The search directions of the bound constrained nonlinear programming problem in the reduced space of the super basic variables are computed by large-scale NLP techniques. A modified Polak-Ribiere conjugate gradient method and a limited storage quasi-Newton BFGS method are analyzed and modifications to deal with the bounds on the variables are suggested based on projected gradient devices with specific linesearches. Some practical models are presented for electric generation planning and fishery management, and the application of the code GRECO - Gradient REduit pour la Commande Optimale - is discussed.
Institute of Scientific and Technical Information of China (English)
WANG Rouhuai
2006-01-01
The main aim of this paper is to discuss the problem concerning the analyticity of the solutions of analytic non-linear elliptic boundary value problems.It is proved that if the corresponding first variation is regular in Lopatinski(i) sense,then the solution is analytic up to the boundary.The method of proof really covers the case that the corresponding first variation is regularly elliptic in the sense of Douglis-Nirenberg-Volevich,and hence completely generalize the previous result of C.B.Morrey.The author also discusses linear elliptic boundary value problems for systems of ellip tic partial differential equations where the boundary operators are allowed to have singular integral operators as their coefficients.Combining the standard Fourier transform technique with analytic continuation argument,the author constructs the Poisson and Green's kernel matrices related to the problems discussed and hence obtain some representation formulae to the solutions.Some a priori estimates of Schauder type and Lp type are obtained.
Modeling Granular Materials as Compressible Non-Linear Fluids: Heat Transfer Boundary Value Problems
Energy Technology Data Exchange (ETDEWEB)
Massoudi, M.C.; Tran, P.X.
2006-01-01
We discuss three boundary value problems in the flow and heat transfer analysis in flowing granular materials: (i) the flow down an inclined plane with radiation effects at the free surface; (ii) the natural convection flow between two heated vertical walls; (iii) the shearing motion between two horizontal flat plates with heat conduction. It is assumed that the material behaves like a continuum, similar to a compressible nonlinear fluid where the effects of density gradients are incorporated in the stress tensor. For a fully developed flow the equations are simplified to a system of three nonlinear ordinary differential equations. The equations are made dimensionless and a parametric study is performed where the effects of various dimensionless numbers representing the effects of heat conduction, viscous dissipation, radiation, and so forth are presented.
Analytical approximate technique for strongly nonlinear oscillators problem arising in engineering
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Y. Khan
2012-12-01
Full Text Available In this paper, a novel method called generalized of the variational iteration method is presented to obtain an approximate analytical solution for strong nonlinear oscillators problem associated in engineering phenomena. This approach resulted in the frequency of the motion as a function of the amplitude of oscillation. It is determined that the method works very well for the whole range of parameters and an excellent agreement is demonstrated and discussed between the approximate frequencies and the exact one. The most significant features of this method are its simplicity and excellent accuracy for the whole range of oscillation amplitude values. Also, the results reveal that this technique is very effective and convenient for solving conservative oscillatory systems with complex nonlinearities. Results obtained by the proposed method are compared with Energy Balance Method (EBM and exact solution showed that, contrary to EBM, simply one or two iterations are enough for obtaining highly accurate results.
Initial-value problem for the Gardner equation applied to nonlinear internal waves
Rouvinskaya, Ekaterina; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim
2017-04-01
The Gardner equation is a fundamental mathematical model for the description of weakly nonlinear weakly dispersive internal waves, when cubic nonlinearity cannot be neglected. Within this model coefficients of quadratic and cubic nonlinearity can both be positive as well as negative, depending on background conditions of the medium, where waves propagate (sea water density stratification, shear flow profile) [Rouvinskaya et al., 2014, Kurkina et al., 2011, 2015]. For the investigation of weakly dispersive behavior in the framework of nondimensional Gardner equation with fixed (positive) sign of quadratic nonlinearity and positive or negative cubic nonlinearity {eq1} partial η/partial t+6η( {1± η} )partial η/partial x+partial ^3η/partial x^3=0, } the series of numerical experiments of initial-value problem was carried out for evolution of a bell-shaped impulse of negative polarity (opposite to the sign of quadratic nonlinear coefficient): {eq2} η(x,t=0)=-asech2 ( {x/x0 } ), for which amplitude a and width x0 was varied. Similar initial-value problem was considered in the paper [Trillo et al., 2016] for the Korteweg - de Vries equation. For the Gardner equation with different signs of cubic nonlinearity the initial-value problem for piece-wise constant initial condition was considered in detail in [Grimshaw et al., 2002, 2010]. It is widely known, for example, [Pelinovsky et al., 2007], that the Gardner equation (1) with negative cubic nonlinearity has a family of classic solitary wave solutions with only positive polarity,and with limiting amplitude equal to 1. Therefore evolution of impulses (2) of negative polarity (whose amplitudes a were varied from 0.1 to 3, and widths at the level of a/2 were equal to triple width of solitons with the same amplitude for a 1) was going on a universal scenario with the generation of nonlinear Airy wave. For the Gardner equation (1) with the positive cubic nonlinearity coefficient there exist two one-parametric families of
Mawhin, Jean; Ure??a, Antonio J.
2002-01-01
A generalization of the well-known Hartman-Nagumo inequality to the case of the vector ordinary p-Laplacian and classical degree theory provide existence results for some associated nonlinear boundary value problems.
Directory of Open Access Journals (Sweden)
Ureña Antonio J
2002-01-01
Full Text Available A generalization of the well-known Hartman–Nagumo inequality to the case of the vector ordinary -Laplacian and classical degree theory provide existence results for some associated nonlinear boundary value problems.
Renormalization-group symmetries for solutions of nonlinear boundary value problems
Kovalev, V F
2008-01-01
Approximately 10 years ago, the method of renormalization-group symmetries entered the field of boundary value problems of classical mathematical physics, stemming from the concepts of functional self-similarity and of the Bogoliubov renormalization group treated as a Lie group of continuous transformations. Overwhelmingly dominating practical quantum field theory calculations, the renormalization-group method formed the basis for the discovery of the asymptotic freedom of strong nuclear interactions and underlies the Grand Unification scenario. This paper describes the logical framework of a new algorithm based on the modern theory of transformation groups and presents the most interesting results of application of the method to differential and/or integral equation problems and to problems that involve linear functionals of solutions. Examples from nonlinear optics, kinetic theory, and plasma dynamics are given, where new analytical solutions obtained with this algorithm have allowed describing the singular...
Nonlinear Inverse Problem for an Ion-Exchange Filter Model: Numerical Recovery of Parameters
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Balgaisha Mukanova
2015-01-01
Full Text Available This paper considers the problem of identifying unknown parameters for a mathematical model of an ion-exchange filter via measurement at the outlet of the filter. The proposed mathematical model consists of a material balance equation, an equation describing the kinetics of ion-exchange for the nonequilibrium case, and an equation for the ion-exchange isotherm. The material balance equation includes a nonlinear term that depends on the kinetics of ion-exchange and several parameters. First, a numerical solution of the direct problem, the calculation of the impurities concentration at the outlet of the filter, is provided. Then, the inverse problem, finding the parameters of the ion-exchange process in nonequilibrium conditions, is formulated. A method for determining the approximate values of these parameters from the impurities concentration measured at the outlet of the filter is proposed.
Institute of Scientific and Technical Information of China (English)
高自友; 贺国平; 吴方
1997-01-01
For current sequential quadratic programming (SQP) type algorithms, there exist two problems; (i) in order to obtain a search direction, one must solve one or more quadratic programming subproblems per iteration, and the computation amount of this algorithm is very large. So they are not suitable for the large-scale problems; (ii) the SQP algorithms require that the related quadratic programming subproblems be solvable per iteration, but it is difficult to be satisfied. By using e-active set procedure with a special penalty function as the merit function, a new algorithm of sequential systems of linear equations for general nonlinear optimization problems with arbitrary initial point is presented This new algorithm only needs to solve three systems of linear equations having the same coefficient matrix per iteration, and has global convergence and local superlinear convergence. To some extent, the new algorithm can overcome the shortcomings of the SQP algorithms mentioned above.
Institute of Scientific and Technical Information of China (English)
胡云卿; 刘兴高; 薛安克
2014-01-01
This paper considers dealing with path constraints in the framework of the improved control vector it-eration (CVI) approach. Two available ways for enforcing equality path constraints are presented, which can be di-rectly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the l1 penalty function and a novel smoothing technique are in-troduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algo-rithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reactor operation problem are in agreement with the literature reports, and the computational efficiency is also high.
Nonlinear gauge interactions: a possible solution to the "measurement problem" in quantum mechanics
Hansson, Johan
2010-01-01
Two fundamental, and unsolved problems in physics are: i) the resolution of the "measurement problem" in quantum mechanics ii) the quantization of strongly nonlinear (nonabelian) gauge theories. The aim of this paper is to suggest that these two problems might be linked, and that a mutual, simultaneous solution to both might exist. We propose that the mechanism responsible for the "collapse of the wave function" in quantum mechanics is the nonlinearities already present in the theory via nonabelian gauge interactions. Unlike all other models of spontaneous collapse, our proposal is, to the best of our knowledge, the only one which does not introduce any new elements into the theory. A possible experimental test of the model would be to compare the coherence lengths - here defined as the distance over which quantum mechanical superposition is still valid - for, \\textit{e.g}, electrons and photons in a double-slit experiment. The electrons should have a finite coherence length, while photons should have a much ...
Park, Y. C.; Chang, M. H.; Lee, T.-Y.
2007-06-01
A deterministic global optimization method that is applicable to general nonlinear programming problems composed of twice-differentiable objective and constraint functions is proposed. The method hybridizes the branch-and-bound algorithm and a convex cut function (CCF). For a given subregion, the difference of a convex underestimator that does not need an iterative local optimizer to determine the lower bound of the objective function is generated. If the obtained lower bound is located in an infeasible region, then the CCF is generated for constraints to cut this region. The cutting region generated by the CCF forms a hyperellipsoid and serves as the basis of a discarding rule for the selected subregion. However, the convergence rate decreases as the number of cutting regions increases. To accelerate the convergence rate, an inclusion relation between two hyperellipsoids should be applied in order to reduce the number of cutting regions. It is shown that the two-hyperellipsoid inclusion relation is determined by maximizing a quadratic function over a sphere, which is a special case of a trust region subproblem. The proposed method is applied to twelve nonlinear programming test problems and five engineering design problems. Numerical results show that the proposed method converges in a finite calculation time and produces accurate solutions.
Institute of Scientific and Technical Information of China (English)
Shuang Ping TAO; Shang Bin CUI
2005-01-01
This paper is devoted to studying the initial value problems of the nonlinear KaupKupershmidt equations (e)u/(e)t + α1u(e)2u/(e)x2+β(e)3u/(e)x3+γ(e)5u/( )x5= 0, (x, t) ∈ R2, and (e)u/(e)t+α2 (e)u/(e)x (e)2u/(e)x2+β(e)3u/(e)x3+γ(e)5u/(e)x5 = 0, (x, t) ∈R2. Several important Strichartz type estimates for the fundamental solution of the corresponding linear problem are established. Then we apply such estimates to prove the local and global existence of solutions for the initial value problems of the nonlinear Kaup-Kupershmidt equations. The results show that a local solution exists if the initial function u0(x) ∈ Hs(R), and s ≥ 5/4 for the first equation and s ≥ 301/108 for the second equation.
Kong, Chao; Hai, Kuo; Tan, Jintao; Chen, Hao; Hai, Wenhua
2016-03-01
Nonlinear Kronig-Penney model has been frequently employed to study transmission problem of electron wave in a doped semiconductor superlattice or in a nonlinear electrified chain. Here from an integral equation we derive a novel exact solution of the problem, which contains a simple nonlinear map connecting transmission coefficient with system parameters. Consequently, we propose a scheme to manipulate electronic distribution and transmission by adjusting the system parameters. A new quantum coherence effect is evidenced by the strict expression of transmission coefficient, which results in the aperiodic electronic distributions and different transmission coefficients including the approximate zero transmission and total transmission, and the multiple transmissions. The method based on the concise exact solution can be applied directly to some nonlinear cold atomic systems and a lot of linear Kronig-Penney systems, and also can be extended to investigate electronic transport in different discrete nonlinear systems.
Generalized Dirichlet Normal Ordering in Open Bosonic Strings
Institute of Scientific and Technical Information of China (English)
CAO Zhen-Bin; DUAN Yi-Shi
2009-01-01
Generally, open string boundary conditions play a nontrivial role in string theory. For example, in the presence of an antisymmetric tensor background field, they will lead the spacetime coordinates noncommutative. In this paper, we mainly discuss how to build up a generalized Dirichlet normal ordered product of open bosonic string embedding operators that satisfies both the equations of motion and the generalized Dirichlet boundary conditions at the quantum level in the presence of an antisymmetric background field, as the generalized Neumann case has already been discussed in the literature. Further, we also give a brief cheek of the consistency of the theory under the newly introduced normal ordering.
Statistical model of stress corrosion cracking based on extended form of Dirichlet energy: Part 2
Indian Academy of Sciences (India)
HARRY YOSH
2016-10-01
In the previous paper ({\\it Pramana – J. Phys.} 81(6), 1009 (2013)), the mechanism of stress corrosion cracking (SCC) based on non-quadratic form of Dirichlet energy was proposed and its statistical features were discussed. Following those results, we discuss here how SCC propagates on pipe wall statistically. It reveals that SCC growth distribution is described with Cauchy problem of time-dependent first-order partial differential equation characterized by the convolution of the initial distribution of SCC over time. We also discuss the extension of the above results to the SCC in two-dimensional space and its statistical features with a simple example.
Global well-posedness for nonlinear nonlocal Cauchy problems arising in elasticity
Directory of Open Access Journals (Sweden)
Hantaek Bae
2017-02-01
Full Text Available In this article, we prove global well-posedness for a family of one dimensional nonlinear nonlocal Cauchy problems arising in elasticity. We consider the equation $$ u_{tt}-\\delta Lu_{xx}=\\big(\\beta \\ast [(1-\\deltau+u^{2n+1}]\\big_{xx}\\,, $$ where $L$ is a differential operator, $\\beta$ is an integral operator, and $\\delta =0$ or 1. (Here, the case $\\delta=1$ represents the additional doubly dispersive effect. We prove the global well-posedness of the equation in energy spaces.
The exact solutions of nonlinear problems by Homotopy Analysis Method (HAM
Directory of Open Access Journals (Sweden)
Hafiz Abdul Wahab
2016-06-01
Full Text Available The present paper presents the comparison of analytical techniques. We establish the existence of the phenomena of the noise terms in the perturbation series solution and find the exact solution of the nonlinear problems. If the noise terms exist, the Homotopy Analysis method gives the same series solution as in Adomian Decomposition Method as well as homotopy Perturbation Method (Wahab et al, 2015 and we get the exact solution using the initial guess in Homotopy Analysis Method using the results obtained by Adomian Decomposition Method.
Smoothing Newton Algorithm for Nonlinear Complementarity Problem with a P* Function
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
By using a smoothing function, the P* nonlinear complementarity problem (P* NCP) can be reformulated as a parameterized smooth equation. A Newton method is proposed to solve this equation. The iteration sequence generated by the proposed algorithm is bounded and this algorithm is proved to be globally convergent under an assumption that the P* NCP has a nonempty solution set. This assumption is weaker than the ones used in most existing smoothing algorithms. In particular, the solution obtained by the proposed algorithm is shown to be a maximally complementary solution of the P* NCP without any additional assumption.
THE DEMAND DISRUPTION MANAGEMENT PROBLEM FOR A SUPPLY CHAIN SYSTEM WITH NONLINEAR DEMAND FUNCTIONS
Institute of Scientific and Technical Information of China (English)
Minghui XU; Xiangtong QI; Gang YU; Hanqin ZHANG; Chengxiu GAO
2003-01-01
This paper addresses the problem of handling the uncertainty of demand in aone-supplier-one-retailer supply chain system. Demand variation often makes the real productiondifferent from what is originally planned, causing a deviation cost from the production plan. Assumethe market demand is sensitive to the retail price in a nonlinear form, we show how to effectivelyhandle the demand uncertainty in a supply chain, both for the case of centralized-decision-makingsystem and the case of decentralized-decision-making system with perfect coordination.
ALE Fractional Step Finite Element Method for Fluid-Structure Nonlinear Interaction Problem
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.
New implicit method for analysis of problems in nonlinear structural dynamics
Directory of Open Access Journals (Sweden)
Gholampour A. A.
2011-06-01
Full Text Available In this paper a new method is proposed for direct time integration of nonlinear structural dynamics problems. In the proposed method the order of time integration scheme is higher than the conventional Newmark’s family of methods. This method assumes second order variation of the acceleration at each time step. Two variable parameters are used to increase the stability and accuracy of the method. The result obtained from this new higher order method is compared with two implicit methods; namely the Wilson-θ and the Newmark’s average acceleration methods.
A NEW SQP-FILTER METHOD FOR SOLVING NONLINEAR PROGRAMMING PROBLEMS
Institute of Scientific and Technical Information of China (English)
Duoquan Li
2006-01-01
In [4],Fletcher and Leyffer present a new method that solves nonlinear programming problems without a penalty function by SQP-Filter algorithm. It has attracted much attention due to its good numerical results. In this paper we propose a new SQP-Filter method which can overcome Maratos effect more effectively. We give stricter acceptant criteria when the iterative points are far from the optimal points and looser ones vice-versa. About this new method,the proof of global convergence is also presented under standard assumptions. Numerical results show that our method is efficient.
SOLUTION OF NONLINEAR PROBLEMS IN WATER RESOURCES SYSTEMS BY GENETIC ALGORITHM
Directory of Open Access Journals (Sweden)
Ahmet BAYLAR
1998-03-01
Full Text Available Genetic Algorithm methodology is a genetic process treated on computer which is considering evolution process in the nature. The genetic operations takes place within the chromosomes stored in computer memory. By means of various operators, the genetic knowledge in chromosomes change continuously and success of the community progressively increases as a result of these operations. The primary purpose of this study is calculation of nonlinear programming problems in water resources systems by Genetic Algorithm. For this purpose a Genetic Algoritm based optimization program were developed. It can be concluded that the results obtained from the genetic search based method give the precise results.
Tang, Yao-Zong; Li, Xiao-Lin
2017-03-01
We first give a stabilized improved moving least squares (IMLS) approximation, which has better computational stability and precision than the IMLS approximation. Then, analysis of the improved element-free Galerkin method is provided theoretically for both linear and nonlinear elliptic boundary value problems. Finally, numerical examples are given to verify the theoretical analysis. Project supported by the National Natural Science Foundation of China (Grant No. 11471063), the Chongqing Research Program of Basic Research and Frontier Technology, China (Grant No. cstc2015jcyjBX0083), and the Educational Commission Foundation of Chongqing City, China (Grant No. KJ1600330).
Directory of Open Access Journals (Sweden)
Slavica M. Perovich
2011-06-01
Full Text Available The subject of the theoretical analysis presented in this paper is an analytical approach to the temperature estimation, as an inverse problem, for different thermistors – linear resistances structures: series and parallel ones, by the STFT - Special Trans Functions Theory (S.M. Perovich. The mathematical formulae genesis of both cases is given. Some numerical and graphical simulations in MATHEMATICA program have been realized. The estimated temperature intervals for strongly determined values of the equivalent resistances of the nonlinear structures are given, as well.
A Reduced Basis Framework: Application to large scale non-linear multi-physics problems
Directory of Open Access Journals (Sweden)
Daversin C.
2013-12-01
Full Text Available In this paper we present applications of the reduced basis method (RBM to large-scale non-linear multi-physics problems. We first describe the mathematical framework in place and in particular the Empirical Interpolation Method (EIM to recover an affine decomposition and then we propose an implementation using the open-source library Feel++ which provides both the reduced basis and finite element layers. Large scale numerical examples are shown and are connected to real industrial applications arising from the High Field Resistive Magnets development at the Laboratoire National des Champs Magnétiques Intenses.
A (k, n-k) Conjugate Boundary Value Problem with Semip ositone Nonlinearity
Institute of Scientific and Technical Information of China (English)
Yao Qing-liu; Shi Shao-yun
2015-01-01
The existence of positive solution is proved for a (k, n−k) conjugate boundary value problem in which the nonlinearity may make negative values and may be singular with respect to the time variable. The main results of Agarwal et al. (Agarwal R P, Grace S R, O’Regan D. Semipositive higher-order differential equa-tions. Appl. Math. Letters, 2004, 14: 201–207) are extended. The basic tools are the Hammerstein integral equation and the Krasnosel’skii’s cone expansion-compression technique.
Morrey Regularity of the Solution to the Dirichlet Problem
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
@@To study the local regularity of solutions to second orderelliptic partial differential equations, Morrey in ［1］ introduced somefunction spaces, which are called the Morrey spaces today. Since then, manymathematicians have studied regularities of solutions to some kinds of secondorder elliptic equations in Morrey spaces.
Institute of Scientific and Technical Information of China (English)
Chongwen Wang; Xing Chu; Weiyao Lan
2014-01-01
Transient performance for output regulation problems of linear discrete-time systems with input saturation is addressed by using the composite nonlinear feedback (CNF) control tech-nique. The regulator is designed to be an additive combination of a linear regulator part and a nonlinear feedback part. The linear regulator part solves the regulation problem independently which produces a quick output response but large oscil ations. The non-linear feedback part with wel-tuned parameters is introduced to improve the transient performance by smoothing the oscil atory convergence. It is shown that the introduction of the nonlinear feedback part does not change the solvability conditions of the linear discrete-time output regulation problem. The effectiveness of transient improvement is il ustrated by a numeric example.