Travelling wave solutions in a negative nonlinear diffusion-reaction model

TL;DR

This paper proves the existence of smooth travelling wave solutions in a nonlinear diffusion-reaction model with logistic kinetics, analyzing their stability and determining the minimum wave speed using a geometric approach.

Contribution

It introduces a geometric method to establish the existence of travelling waves in a model with sign-changing nonlinear diffusivity and explores their spectral stability.

Findings

Existence of smooth travelling wave solutions proven.

Minimum wave speed c* determined.

Relation between wave speed and spectral stability analyzed.

Abstract

We use a geometric approach to prove the existence of smooth travelling wave solutions of a nonlinear diffusion-reaction equation with logistic kinetics and a convex nonlinear diffusivity function which changes sign twice in our domain of interest. We determine the minimum wave speed, c*, and investigate its relation to the spectral stability of the travelling wave solutions.