具有分布时滞的一类反应扩散方程的波前解的存在性（英文）

The Existence of Traveling Wave Fronts for A Reaction-Diffusion Equation with Distributed Delays

本文考虑了一类广义分布时滞下的反应扩散方程的行波解的存在性问题。运用几何奇异摄动理论和线性链方法,我们研究了反应扩散方程若在没有时滞情形下具有行波解,则只要平均时滞充分小,所给的广义时滞核下这个行波解可以保持存在.

In this work,the existence of traveling wave solutions of a reactiondiffusion equation with generalized distributed delays is considered.Under this generalized delay kernels,by employing the linear chain trick and the geometric singular perturbation theory,we investigate a natural connection between the existence of traveling wave solutions for the reaction-diffusion equation with distributed delays and the existence of traveling wave solutions for the corresponding reaction-diffusion equation without delay.It was shown that if the corresponding reaction-diffusion equation without delay has a traveling wave solution,then,for sufficiently small average delay,the delayed reaction-diffusion equation also has a traveling wave solution.