Existence of traveling wave front for a generalized reaction-convection-diffusion equation

Abstract

In presented paper, the existence of traveling wave front for a generalized reaction-convection-diffusion equation with different delay convolution kernels is investigated by using the geometric singular perturbation theory. Firstly, we shall show that such traveling wave front exists without delay by qualitative analysis. After that, for the generalized reaction-convection-diffusion equation with a special local strong delay convolution kernel, the desired heteroclinic orbit is obtained by constructing a locally invariant manifold. Finally, with a nonlocal weak generic delay, the existence of traveling wave front is proved by implicit function theorem and Fredholm theory.