Pulsating fronts for bistable on average reaction-diffusion equations in a time periodic environment

TL;DR

This paper investigates pulsating front solutions in time-periodic reaction-diffusion equations with bistable nonlinearities, establishing existence, uniqueness, monotonicity, and stability under certain conditions.

Contribution

It proves the existence of pulsating fronts for small periods and perturbations, extending understanding of wave solutions in time-periodic bistable systems.

Findings

Existence of pulsating fronts for small periods

Uniqueness and monotonicity of solutions

Stability analysis of pulsating fronts

Abstract

This paper is devoted to reaction-diffusion equations with bistable nonlinearities depending periodically on time. These equations admit two linearly stable states. However, the reaction terms may not be bistable at every time. These may well be a periodic combination of standard bistable and monostable nonlinearities. We are interested in a particular class of solutions, namely pulsating fronts. We prove the existence of such solutions in the case of small time periods of the nonlinearity and in the case of small perturbations of a nonlinearity for which we know there exist pulsating fronts. We also study uniqueness, monotonicity and stability of pulsating fronts.