一般柱形边界区分场的谱方法计算

本文设计了一种计算方法,使谱方法可用于一般边界问题,方法分两步:1.用谱方法解具有简单边界的方程;2、修正复杂边界处的解以满足边界条件。算例是孤立波绕椭圆柱的问题,计算结果显示为不同时刻的二维等值线图与三维波动图。     

A NEW VARIATIONAL INEQUALITY FORMULATION FOR SEEPAGE PROBLEMS WITH FREE SURFACES

IntroductionTherearetwoclassesofsolutionsforseepageproblemswithfreesurfaces ,i.e .,theadaptivemeshmethodsandthefixedmeshmethods.Theadaptivemeshmethodsinvolvetoolargeamountofcomputationforinhomogeneoussoilsandoftenleadtodivergentcalculations,andhence,arenowbeingsupercededbythefixedmeshmethods.Thefixedmeshmethodsfallintotwocategories,theintuitivemethodsandthevariationalinequalitymethods.Theintuitivemethods[1- 3]establishusuallytheiterativeproceduresbaseduponthefactthatthereisnodischargebetweenth…     

对一类涉及电场边界问题的商讨

我们常常在一些联考和大型考试中发现有这样一类型的题目,往往还是最后的压卷题,在电场的边界模型上出现了问题,或没有引起重视而导致一些错误．下面举几个例子,和同行们共同商讨,抛砖引玉．     

A closed form solution to one dimensional robin boundary problems

Many cellular and subcellular biological processes can be described in terms of diffusing and chem- ically reacting species (e.g. enzymes). In this paper, we will use reflected and absorbed Brownian motion and stochastic differential equations to construct a closed form solution to one dimensional Robin boundary prob- lems. Meanwhile, we will give a reasonable explanation to the closed form solution from a stochastic point of view. Finally, we will extend the problem to Robin boundary problem with two boundary conditions and give a specific solution by resorting to a stopping time.     

INVERSE SCATTERING PROBLEMS BY SINGULAR SOURCE METHODS

The inverse scattering problems are to detect the property of obstacles from the measurements outside the obstacles. One of important research areas in this topic is the recovery of boundary property for impenetrable obstacles. In this paper, we would like to give a brief review about the recently developed singular source methods. There are three different methods in this category, namely, linear sampling method, pointsource method and probe method. We also present some recent new results about the probe method.     

用同伦方法求Picard边值问题的解

This paper deals with the problem of finding solutions to the Picard boundary problem. In our approach, by means of the homotopy method, the equation considered is linked to a simpler equation by introducing a parameter. We first find the solutions of the simpler equation, and give a priori estimates of" the equa tion we considered, and then one can obtain the solutions of Picard boundary problem by following the path of solutions of Cauchy problem.     

Maslov P-Index Theory for a Symplectic Path with Applications

Abstract The Maslov P-index theory for a symplectic path is defined. Various properties of this index theory such as homotopy invariant, symplectic additivity and the relations with other Morse indices are studied. As an application, the non-periodic problem for some asymptotically linear Hamiltonian systems is considered. *Project supported by the National Natural Science Foundation of China (No.10531050) and FANEDD.     

Analysis of a Free Boundary Problem Modeling Tumor Growth

In this paper, we study a free boundary problem arising from the modeling of tumor growth. The problem comprises two unknown functions： R = R（t）, the radius of the tumor, and u = u（r, t）, the concentration of nutrient in the tumor. The function u satisfies a nonlinear reaction diffusion equation in the region 0 〈 r 〈 R（t）, t 〉 0, and the function R satisfies a nonlinear integrodifferential equation containing u. Under some general conditions, we establish global existence of transient solutions, unique existence of a stationary solution, and convergence of transient solutions toward the stationary solution as t →∞.     

地下水渗流自由边界问题的分裂隐处理方法

1 引言 地下水是一种极其重要的资源,也是人类赖以生存的环境,不仅水资源的开发利用情况直接关系到国民经济的发展,而且水资源的保护也是保护人类生存环境的重要组成部分.在地下水渗流过程中,自由潜水面、自由交界面问题的计算一直是非常困难的问题,本文讨论多孔介质饱和带中均质地下水渗流自由边界问题的一类数值方法:分裂—隐处理方法,对—维入渗补给问题给出严格的理论分析,证明了最优阶误差估计(L~2,H~1,H~2模). 2 数学模型 研究地下渗流问题的方法通常采用Euler方法.取体积元ΔV=ΔxΔyΔz,在该体积     

THE EXISTENCE AND THE NON-EXISTENCE OF GLOBAL SOLUTIONS OF A FREE BOUNDARY PROBLEM

We study a free boundary problem of parabolic equations with a positive parameter τ included in the coefficient of the derivative with respect to the time variable t. This problem arises from some reaction-diffusion system. We prove that, if τ is large enough, the solution exists for 0<t<+∞;while, if τ is small enough, the solution exists only in finite time.