Lyapunov stability of planar waves to the reaction-diffusion equation with a non-Lipschitzian reaction term
type: Item
instance of: scholarly article
title: Lyapunov stability of planar waves to the reaction-diffusion equation with a non-Lipschitzian reaction term
zbMATH Open document ID: 1479.35078
DOI: 10.1155/2021/7756150
author: Soyeun Jung
author: Eunkyung Ko
published in: Advances in Mathematical Physics
publication date: 2021-11-25T00:00:00Z
review text: Summary: Extending [\textit{P. Drábek} and \textit{P. Takáč}, J. Math. Biol. 75, No. 4, 929--972 (2017; Zbl 1378.35311)], we investigate the Lyapunov stability of planar waves for the reaction-diffusion equation on \(\mathbb{R}^n\), \(n\geq2\), with a \(\alpha\)-Hölder continuous (\(0<\alpha<1\)), 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.
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 7433508
zbMATH Keywords: sub- and supersolutions technique
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/7756150
OpenAlex ID: W3205154155
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description: scientific article; zbMATH DE number 7433508