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