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Lyapunov Stability of Planar Waves to the Reaction-Diffusion Equation with a Non-Lipschitzian Reaction Term

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  • Soyeun Jung
  • Eunkyung Ko

Abstract

Extending (Drábek and TakÃ¡Ä 2017), we investigate the Lyapunov stability of planar waves for the reaction-diffusion equation on , , with a - H lder continuous ( ), but not necessarily smooth reaction term. We first consider an initial value problem for the equation and then construct sub- and supersolutions to the problem by a subtle modification of the planar wave. Our main result states that a bounded classical solution to the problem stays near the planar wave for all time whenever an initial data is close enough to the planar wave.

Suggested Citation

  • Soyeun Jung & Eunkyung Ko, 2021. "Lyapunov Stability of Planar Waves to the Reaction-Diffusion Equation with a Non-Lipschitzian Reaction Term," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-10, October.
    • Handle: RePEc:hin:jnlamp:7756150
    DOI: 10.1155/2021/7756150
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