一类具强非线性源的热方程解的存在性  

The Existence of the Solutions for a Class of Semilinear Heat Equations with Strong Nonlinear Sources

作　　者：胡文燕[1] 

机构地区：[1]晋中学院数学学院,山西晋中030619

出　　处：《晋中学院学报》2016年第3期17-19,共3页Journal of Jinzhong University

摘　　要：对一类具强非线性源的热方程的初边值问题,可应用Leray-Schauder拓扑度理论对其解的存在性进行研究.利用Leray-Schauder度的基本性质定理和拓扑度方法,以非齐热方程的古典解理论为基础,证明了其初边值问题解的存在性.For the initial boundary value problem of a class of strongly nonlinear source of heat equation, Leray Schauder topological degree theory can be used to study the existence of the solutions. With the basic property theorem of the Leray Schauder degrees and the method of topological degree, the article proves the existence of the solution to the initial-boundary value problem in a neat heat equation based on the theory of classical solution.

关 键 词：强非线性源 LERAY-SCHAUDER度 拓扑度理论 存在性 

分 类 号：O175.23[理学—数学]