March 3, 2026Open Access

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

Key Points

Convergence to traveling waves occurs if initial data is close to a wave profile at infinity, leading to stability.
The analysis highlights the use of Lyapunov-type arguments in understanding reaction-diffusion systems.
Results apply primarily to predator-prey systems with specific examples demonstrating wave stability.
Implications suggest robust behavior of solutions, enhancing the understanding of complex dynamical systems.

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.

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Authors

Arnaud Ducrot

Université Le Havre Normandie

Masahiko Shimojō

Tokyo Metropolitan University

Journals

Journal of Dynamics and Differential Equations

Actions

Institutions

Tokyo Metropolitan University

Normandie Université

Université Le Havre Normandie

References and Citations

Connected Papers

Building similarity graph...

Analyzing shared references across papers

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

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Authors

Journals

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

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