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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月5日

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  • Arnaud Ducrot,
  • Masahiko Shimojo

摘要

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.