Convergence to Traveling Waves for Reaction-Diffusion Systems using Lyapunov Type Arguments

Read full text
Authors: Arnaud Ducrot, Masahiko Shimojō
Cited by: 1
References: 28

Abstract

This paper investigates the convergence of certain solutions of reaction-diffusion systems to traveling waves. Using Lyapunov-type arguments, we show that if the initial data is sufficiently close to a wave profile at infinity, then the solution converges to this special solution as time tends to infinity. We apply this theory to predator-prey systems and, in particular, prove the stability of traveling waves for several specific examples.

Fields of Study & Subjects

Mathematical and Theoretical Epidemiology and Ecology Models Mathematical Biology Tumor Growth Stability and Controllability of Differential Equations

Publication details

Journal / source
Journal of Dynamics and Differential Equations
Publisher
Springer Science and Business Media LLC
Publication date
5 February 2026
Language
EN