三类多双曲复方程组的Riemann-Hilbert边值问题

用函数论的方法研究了三类超定双曲型方程组的解,即三类多双曲复方程组在一般柱形域上的Riemann-Hilbert边值问题的提法,可解条件,解的表示,唯一性和存在性.     

某些一阶双曲方程组的初边值问题

本文利用函数论的方法,讨论了R3和R4空间中的一阶双曲型方程组的初边值问题,在不同情况下,分别获得了可解条件和解的表示.     

二维热传导型半导体问题的一个二阶格式

热传导型半导体器件瞬态问题的数学模型由四个拟线性偏微分方程所组成的方程组的初边值问题来描述。其中电子位势方程是椭圆型的,电子和空穴浓度方程是对流扩散型的,温度方程为热传导型的。本文对二维热传导型半导体的一类混合初边值问题利用降阶法给出了一个二阶差分格式,并对其进行了详细的理论分析,得到了离散的犾２ 误差估计结果。     

利用Prüfer变换求解微分方程

针对一类二阶非线性常微分方程,利用Prüfer变换将其约化为特殊的一阶常微分方程组,从而使其求解过程得以简化.实例说明应用Prüfer变换求解一类偏微分方程边值问题的技巧.     

E2类二阶椭圆组一般形式的非线性边值问题

研究了E2类二阶椭圆型方程组相当广泛的一类非线性边值问题，通过引进一种代换把它化为一类非线性广义Riemann-Hilbert边值问题，再引进奇异积分算子，建立与该问题等价的非线性奇异积分方程。应用奇异积分算子性质和泛函分析与函数论方法，在一定的假设条件下，证得了该问题的可解性。     

利用对称方法求解非线性偏微分方程组边值问题的数值解

本文研究微分方程对称方法在非线性偏微分方程组边值问题中的应用.首先,利用吴-微分特征列集算法确定给定非线性偏微分方程组边值问题的多参数对称;其次,利用对称将非线性偏微分方程组边值问题约化为常微分方程组初值问题;最后,利用龙格-库塔法求解常微分方程组初值问题的数值解.     

同伦摄动法在求解四阶边值问题中的应用

将同伦摄动法用于求解常微分方程四阶边值问题.通过将常微分方程边值问题转化为积分方程组,应用同伦摄动法求得近似解.给出同伦摄动法在两个具体的实例中的应用,并将近似解与精确解进行了比较,验证了同伦摄动法对求解线性、非线性常微分方程边值问题是一种非常有效的方法.     

一类强非线性偏微分方程组初边值问题之逆算符解法新探

对填充床催化反应器的数学模型──一类强非线性偏微分方程级─边值问题,用逆算符法求其近似解析解,提出了用“部分解的几何平均”替代“部分解的算术平均”的新方法．从而较园满地给出了此类方程组初─边值问题的近似解析解．     

一维抛物型方程源项反问题的数值求解

<正>1引言近些年来,为适应科学和经济的发展,对于偏微分方程边值问题的研究从低维到高维,线性到非线性,单个方程到方程组不断发展并逐步拓宽和延伸.如热传导、材料学、流体学、图像处理和数学物理及工程科学中都涉及了此类方程.大量的抛物型方程反问题在     

两维完全非线性伪抛物组的差分格式

用差分法研究两维完全非线性伪抛物型偏微分方程组的初边值问题,利用不动点原理和先验估计,证明了差分方程组离散向量解的存在唯一性,收敛性和稳定性.这里假定原来的完全非线性伪抛物组存在唯一光滑解。根据这种方法,对三维完全非线性伪抛物组可证明类似的结果成立,并且在一维情形,改进了已有的结果.     

Noncoercive Boundary Value Problems for Elliptic Partial Differential and Differential-Operator Equations

In this paper we find conditions guarantee that irregular boundary value problems for elliptic differential-operator equations of the second order in an interval are fredholm. We apply this result to find some algebraic conditions guarantee that irregular boundary value problems for elliptic partial differential equations of the second order in cylindrical domains are fredholm. Apparently this is the first paper where the regularity of an elliptic boundary value problem is not satisfied on a manifold of the dimension equal to dimension of the boundary. Nevertheless the problem is fredholm and the resolvent is compact. It is interesting to note that the considered boundary value problems for elliptic equations in a cylinder being with separating variables are noncoercive.     

Hopf-Cole transformation to some systems of partial differential equations

In this paper we study a system of nonlinear partial differential equations which we write as a Burgers equation for matrix and use the Hopf-Cole transformation to linearize it. Using this method we solve initial value problem and initial boundary value problems for some systems of parabolic partial differential equations. Also we study an initial value problem for a system of nonlinear partial differential equations of first order which does not have solution in the standard distribution sense and construct an explicit solution in the algebra of generalized functions of Colombeau. Received November 1999     

Noncoercive boundary value problems for the Laplace equation with a spectral parameter

In this paper we find conditions that guarantee that irregular boundary value problems for elliptic differential-operator equations of the second order in an interval are coercive with a defect and fredholm; compactness of a resolvent and estimations by spectral parameter; completeness of root functions. We apply this result to find some algebraic conditions that guarantee that irregular boundary value problems for elliptic partial differential equations of the second order in cylindrical domains have the same properties. Apparently this is the first paper where the regularity of an elliptic boundary value problem is not satisfied on a manifold of the dimension equal to the dimension of the boundary. Nevertheless, the problem is fredholm and the resolvent is compact. It is interesting to note that the considered boundary value problems for elliptic equations in a cylinder being with separating variables are noncoercive. I wish to thank the referee whose comments helped me improve the style of the paper. Supported in part by the Israel Ministry of Science and Technology and the Israel-France Rashi Foundation.     

Fredholm property of elliptic boundary value problems for partial differential and differential- operator equations

In this paper we find conditions on boundary value problems for elliptic differential-operator equations of the 4-th order in an interval to be fredholm. Apparently, this is the first publication for elliptic differential-operator equations of the 4-th order, when the principal part of the equation has the form u′?n(t) + Au″(t) + Bu(t), where AB^-1/2 is a bounded operator and is not compact. As an application we find some algebraic conditions on boundary value problems for elliptic partial equations of the 4-th order in cylindrical domains to be fredholm. Note that a new method has actually been suggested here for investigation of boundary value problems for elliptic partial equations of the 4-th order.     

偏微分方程的调和分析方法简介

本文致力于阐述调和分析与现代偏微分方程研究的关系,特别是奇异积分算子、拟微分算子、Fourier限制性估计、Fourier频率分解方法在椭圆边值问题、非线性发展方程研究中的重要作用.对于偏微分方程研究的各种方法进行了比较与分析,指出了偏微分方程的调和分析方法的优点与局限性.与此同时,还给出了偏微分方程的调和分析方法这一领域的最新研究进展.     

A nonlocal boundary value problem for elliptic differential-operator equations and applications

In this paper we give, for the first time, an abstract interpretation of nonlocal boundary value problems for elliptic differential equations of the second order. We prove coerciveness and Fredholmness of nonlocal boundary value problems for the second order elliptic differential-operator equations. We apply then, in section 6, these results for investigation of nonlocal boundary value problems for the second order elliptic differential equations (one can find the references on the subject in the introduction and Chapter V in the book by A. L. Skubachevskii [27]). Abstract results obtained in this paper can be used for study of nonlocal boundary value problems for quasielliptic differential equations.     

Analytical eigenvalue bounds for matrices arising when discretizing the self-adjoint second order elliptic partial differential equations

This paper shows how to derive analytical expressions for the eigenvalue bounds of matrices arising when using a fast method for separable finite difference equations for the numerical solution of the first three boundary value problems for the two-dimensional self-adjoint second order elliptic partial differential equation in a rectangle.     

Fehlerabschätzungen bei Randwertaufgaben partieller Differentialgleichungen mit unendlichem Grundgebiet

Summary Types of boundary value problems of partial differential equations for infinite domains are discussed which can easily be transformed in such a manner as to allow estimations of error (for approximate solutions) similar to the boundary maximum principle. First, second und third boundary value problems for the outer domain of linear elliptic and certain linear and nonlinear parabolic differential equations are examined. For elliptic differential equations one of the results is that the secound boundary value problem for more than two dimensions can be included. The estimates of the paper can thus be applied to problems of flow around some object, not in the case of two but of three dimensions. This is in a certain sense a counterpart to the conformal mappings method which is successful for two but not for three dimensions. Numerical examples show that estimations of error can easily be carried out.     

A class of pseudo-monotone operators and its applications in PDE

In this paper we give a criterion of pseudo-monotone operators by which a class of operators related to elliptic partial differential equations is recognized as pseudo-monotone operators. Some applications in boundary value problems for elliptic equations and obstacle problems are given. Research supported by the Fund of IMAS     

Abstract Elliptic Equations with Integral Boundary Conditons

This paper focuses on nonlocal integral boundary value problems for elliptic differential-operator equations. Here given conditions guarantee that maximal regularity and Fredholmness in $L_{p}$ spaces. These results are applied to the Cauchy problem for abstract parabolic equations, its infinite systems and boundary value problems for anisotropic partial differential equations in mixed $L_{\mathbf{p}}$ norm.