Persistence of pulses for certain reaction-diffusion equations in dimensions two and three

TL;DR

This paper investigates how stationary pulse solutions in reaction-diffusion equations in two and three dimensions persist under perturbations, providing asymptotic approximations to understand their behavior.

Contribution

It offers a detailed analysis of pulse persistence under perturbations and derives leading-order asymptotic approximations in 2D and 3D reaction-diffusion systems.

Findings

Pulse solutions persist under certain perturbations.

Asymptotic approximations accurately describe pulse behavior.

Results applicable to higher-dimensional reaction-diffusion models.

Abstract

We address the persistence under a perturbation of stationary pulse solutions of some reaction-diffusion type equations in dimensions d=2,3 and evaluate the asymptotic approximations of such pulses to the leading order in the parameter of the perturbation.