Nonlinear estimates for traveling wave solutions of reaction diffusion equations

Abstract

In this paper we will establish nonlinear a priori lower and upper bounds for the solutions to a large class of equations which arise from the study of traveling wave solutions of reaction–diffusion equations, and we will apply our nonlinear bounds to the Lotka–Volterra system of two and four competing species as examples. The idea used in a series of papers by the first author et al. for the establishment of the linear N-barrier maximum principle will also be used in the proof.