一类具强非线性源的热方程解的存在性

摘要

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.%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。