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

Soyeun Jung and Eunkyung Ko

Advances in Mathematical Physics, 2021, vol. 2021, 1-10

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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:7756150

DOI: 10.1155/2021/7756150

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