一类具有特殊区域的椭圆型方程奇摄动问题  

A Class of Problems for the Singular Perturbation of Elliptic Equations with Special Domain

作　　者：冯茂春[1] 肖佳妮 王淼坤[1] FENG Maochun;XIAO Jiani;WANG Miaokun(School of Science,Huzhou Normal University,Huzhou 313000,China)

机构地区：[1]湖州师范学院理学院,浙江湖州313000

出　　处：《应用数学》2023年第4期859-867,共9页Mathematica Applicata

基　　金：国家自然科学基金(11701176)。

摘　　要：本文讨论一类带有一阶偏导的椭圆型拟线性方程的奇摄动问题,其变量区域是特殊的三角形区域.由于PDE(偏微分方程)的特殊性,解很复杂.这里摒弃了传统单一的求渐近解的方法,而采用两种方法组合使用,成功求得一致有效的渐近解.首先通过边界层函数法求出边界直线段上的内部解,再将它们与外部解及顶点处的内层解相匹配,求得处处有效的渐近解,并借此解决方程含多重解的问题.In this paper,we discuss the singularly perturbed problem of a class of elliptic quasilinear equations with first-order partial derivatives,whose variable domain is the special triangle domain.Due to the particularity of PDE(partial differential equation),the solutions are very complex.Abandoning the traditional single method of finding asymptotic solution,using the combination of the two different methods,the uniformly effective asymptotic solution is successfully obtained.Firstly,the inner solutions are obtained by the boundary layer function method,and then they are matched with the outer solution and the inner solution at the vertex to obtain the everywhere effective asymptotic solution,so as to solve the problem that the equation contains multiple solutions.

关 键 词：拟线性椭圆型方程 奇异特征 指数型衰减 特异极限 复合渐近解 

分 类 号：O175.29[理学—数学]