Travelling wave solutions of a bistable reaction-diffusion equation with nonlinear jump discontinuity

TL;DR

This paper investigates the existence and stability of travelling wave solutions in a bistable reaction-diffusion equation featuring a nonlinear jump discontinuity, using sub-super solution methods to address the challenges posed by the discontinuity.

Contribution

It introduces a novel analysis of travelling wave solutions in reaction-diffusion equations with nonlinear jump discontinuities, a common feature in reaction-diffusion-ODE systems.

Findings

Established existence of travelling wave solutions

Proved stability of these solutions

Applied sub-super solution method to discontinuous nonlinear terms

Abstract

This paper is concerned with the existence and the stability of travelling wave solutions to a bistable reaction-diffusion equation with a jump discontinuious point on nonlinear term. Sub-super solution method is used throughout this paper. As a matter of fact, this nonlinear discontinuity term is frequently emerging when study the travelling wave solution of reaction-diffusion-ODE systems. Hence, it is meaningful to consider this kind of problem.