一类非线性反应扩散方程的冲击波解

Shock Wave Solutions of A Nonlinear Reaction-Diffusion Equation

本文研究一类非线性反应扩散方程的冲击波解。以扩散系数作为系统的参数 ,通过定性方法分析行波解所满足的常微分方程的异宿轨道的存在性和唯一性 ,得到了这类反应扩散方程的各种冲击波解的存在性和唯一性 。

This paper deals with the shock wave solutions of a nonlinear reaction-diffusion equation. Taken the coefficient of diffusion as a system parameter, the existence and uniqueness of different types of shock waves of the equation are obtained by analyzing qualitatively the existence and uniqueness of the heteroclinic trajectories of the ordinary differential equation satisfied by the travelling wave solutions. Furthermore, the approximate analytic expressions of all types of the shock wave solutions are given by the methods of constructing the solutions to be determined.