Traveling front solutions for perturbed reaction-diffusion equations

Traveling front solutions have been studied for reaction-diffusion equations with various kinds of nonlinear terms. One of the interesting subjects is the existence and non-existence of them. In this paper, we prove that, if a traveling front solution exists for a reaction-diffusion equation with a nonlinear term, it also exists for a reaction-diffusion equation with a perturbed nonlinear term. In other words, a traveling front is robust under perturbation on a nonlinear term.

Mathematics Subject Classification. Primary 35C07; Secondary 35B20, 35K57.