Traveling fronts in balanced bistable reaction-diffusion equations

Abstract

This paper is an announcement of a forthcoming paper [21]. We study axially asymmetric traveling fronts to reaction-diffusion equations with balanced bistable nonlinear terms. We prove such a solution as the balanced limit of a pyramidal traveling front of an imbalanced bistable reaction-diffusion equation by preserving the ratio of a major axis and a minor axis of the cross section to be a constant. When the constant ratio is not one, the limit functions become axially asymmetric traveling fronts to balanced bistable reaction-diffusion equations.