共查询到10条相似文献,搜索用时 109 毫秒
1.
C. Fresneda-Portillo 《复变函数与椭圆型方程》2020,65(4):558-572
ABSTRACTA mixed boundary value problem (BVP) for the diffusion equation in non-homogeneous media partial differential equation is reduced to a system of direct segregated parametrix-based boundary-domain integral equations (BDIEs). We use a parametrix different from the one employed by Mikhailov [Localized boundary-domain integral formulations for problems with variable coefficients. Eng Anal Bound Elem. 2002;26:681–690], Mikhailov and Portillo [A new family of boundary-domain integral equations for a mixed elliptic BVP with variable coefficient. In: Paul Harris, editor. Proceedings of the 10th UK conference on boundary integral methods. Brighton: Brighton University Press; 2015. p. 76–84] and Chkadua, Mikhailov, Natroshvili [Analysis of direct boundary-domain integral equations for a mixed BVP with variable coefficient. I: equivalence and invertibility. J Integral Eqs Appl. 2009;21:499–543]. We prove the equivalence between the original BVP and the corresponding BDIE system. The invertibility and Fredholm properties of the boundary-domain integral operators are also analysed. 相似文献
2.
A Rigorous ODE Solver and Smale's 14th Problem 总被引:9,自引:0,他引:9
Warwick Tucker 《Foundations of Computational Mathematics》2002,2(1):53-117
We present an algorithm for computing rigorous solutions to a large class of ordinary differential equations. The main algorithm
is based on a partitioning process and the use of interval arithmetic with directed rounding. As an application, we prove
that the Lorenz equations support a strange attractor, as conjectured by Edward Lorenz in 1963. This conjecture was recently
listed by Steven Smale as one of several challenging problems for the twenty-first century. We also prove that the attractor
is robust, i.e., it persists under small perturbations of the coefficients in the underlying differential equations. Furthermore,
the flow of the equations admits a unique SRB measure, whose support coincides with the attractor. The proof is based on a
combination of normal form theory and rigorous computations.
July 27, 2000. Final version received: June 30, 2001. 相似文献
3.
COMPARISON AND OSCILLATION THEOREMS FOR AN ADVANCED TYPE DIFFERENCE EQUATIONCOMPARISONANDOSCILLATIONTHEOREMSFORANADVANCEDTYPE... 相似文献
4.
Lászlo Horváth 《Integral Equations and Operator Theory》2003,45(2):155-176
In this paper, we consider a class of integral equations in measure
spaces, and the corresponding integral inequalities. Special cases are Volterra
type integral equations and Gronwall type integral inequalities. We give different
necessary and su.cient, and only su.cient conditions which together
with the Lipschitz condition imply the existence and the uniqueness of solutions
of the considered integral equations. We study the successive approximations
for the considered integral equations. We derive estimates for the
solutions of the studied integral equations and integral inequalities.
Submitted: June 20, 2000?Revised: July 10, 2001 相似文献
5.
A simple direct method is presented to find equivalence transformations of nonlinear mathematical physics equations. By using the direct method, we obtain the continuous equivalence transformations of a class of nonlinear Schröequations with variable coefficients and a family of nonlinear KdV equations with variable coefficients. For the nonlinear Schrödinger equations with variable coefficients, the equivalence transformations obtained by the direct method coincide, in nature, with those obtained via the infinitesimal Lie criterion, but our computation is much simpler. 相似文献
6.
Wang Jianzhong 《数学年刊B辑(英文版)》1994,15(1):23-34
ON SOLUTIONS OF TWO-SCALE DIFFERENCE EQUATIONS ¥WANGJIANZHONGAbstract:Thispaperisconcernedwithsolutionsofthefollowingtwo-scal... 相似文献
7.
A.S. Fokas 《Selecta Mathematica, New Series》1998,4(1):31-68
A new transform method for solving initial-boundary value problems for linear and integrable nonlinear PDEs in two independent
variables has been recently introduced in [1]. For linear PDEs this method involves: (a) formulating the given PDE as the
compatibility condition of two linear equations which, by analogy with the nonlinear theory, we call a Lax pair; (b) formulating
a classical mathematical problem, the so-called Riemann-Hilbert problem, by performing a simultaneous spectral analysis of both equations defining the Lax pair; (c) deriving certain global relations satisfied by the boundary
values of the solution of the given PDE. Here this method is used to solve certain problems for the heat equation, the linearized
Korteweg-deVries equation and the Laplace equation. Some of these problems illustrate that the new method can be effectively
used for problems with complicated boundary conditions such as changing type as well as nonseparable boundary conditions. It is shown that for simple boundary conditions the global relations (c) can be analyzed using only
algebraic manipulations, while for complicated boundary conditions, one needs to solve an additional Riemann-Hilbert problem.
The relationship of this problem with the classical Wiener-Hopf technique is pointed out. The extension of the above results
to integrable nonlinear equations is also discussed. In particular, the Korteweg-deVries equation in the quarter plane is
linearized. 相似文献
8.
Application of the Exp-function method for nonlinear differential-difference equations 总被引:1,自引:0,他引:1
Ahmet Bekir 《Applied mathematics and computation》2010,215(11):4049-9197
In this paper, we established abundant travelling wave solutions for some nonlinear differential-difference equations. It is shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful new method for discrete nonlinear evolution equations in mathematical physics. 相似文献
9.
This paper is the continuation of the paper ``Dirichlet boundary control of semilinear parabolic equations. Part 1: Problems
with no state constraints.' It is concerned with an optimal control problem with distributed and Dirichlet boundary controls
for semilinear parabolic equations, in the presence of pointwise state constraints. We first obtain approximate optimality
conditions for problems in which state constraints are penalized on subdomains. Next by using a decomposition theorem for
some additive measures (based on the Stone—Cech compactification), we pass to the limit and recover Pontryagin's principles
for the original problem.
Accepted 21 July 2001. Online publication 21 December 2001. 相似文献
10.
D. Braess 《Constructive Approximation》2001,17(1):147-151
Although Newman's trick has been mainly applied to the approximation of univariate functions, it is also appropriate for
the approximation of multivariate functions that are encountered in connection with Green's functions for elliptic differential
equations. The asymptotics of the real-valued function on a ball in 2-space coincides with that for an approximation problem
in the complex plane. The note contains an open problem.
May 17, 1999. Date revised: October 20, 1999. Date accepted: March 17, 2000. 相似文献