Travelling wave solutions in a negative nonlinear diffusion–reaction model

Yifei Li, Peter van Heijster*, Robert Marangell, Matthew J. Simpson

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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 a desingularised linear operator associated with the travelling wave solutions.

Original languageEnglish
Pages (from-to)1495–1522
JournalJournal of Mathematical Biology
Volume81
DOIs
Publication statusPublished - Dec 2020

Keywords

  • Geometric methods
  • Nonlinear diffusion
  • Phase plane analysis
  • Spectral stability
  • Travelling wave solutions

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