Multidimensional stability of V-shaped traveling fronts in bistable reaction-diffusion equations with nonlinear convection
This paper is concerned with the multidimensional stability of V-shaped traveling fronts for a reaction-diffusion equation with nonlinear convection term in $\mathbb{R}^n$ ($n\geq3$). We consider two cases for initial perturbations: one is that the initial perturbations decay at space infinity and a...
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doaj-ee79996609644b8fb20019ec1039a3b52020-11-25T03:44:37ZengAIMS PressAIMS Mathematics2473-69882021-10-016131433210.3934/math.2021020Multidimensional stability of V-shaped traveling fronts in bistable reaction-diffusion equations with nonlinear convectionHui-Ling Niu0School of Mathematics and Information Science, North Minzu University, Yinchuan, Ningxia 750021, People’s Republic of ChinaThis paper is concerned with the multidimensional stability of V-shaped traveling fronts for a reaction-diffusion equation with nonlinear convection term in $\mathbb{R}^n$ ($n\geq3$). We consider two cases for initial perturbations: one is that the initial perturbations decay at space infinity and another one is that the initial perturbations do not necessarily decay at space infinity. In the first case, we show that the V-shaped traveling fronts are asymptotically stable. In the second case, we first show that the V-shaped traveling fronts are also asymptotically stable under some further assumptions. At the same time, we also show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which means that the traveling fronts are not asymptotically stable under general bounded perturbations.https://www.aimspress.com/article/10.3934/math.2021020/fulltext.htmlreaction-diffusion equationnonlinear convectionv-shaped traveling frontmultidimensional stability |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Hui-Ling Niu |
spellingShingle |
Hui-Ling Niu Multidimensional stability of V-shaped traveling fronts in bistable reaction-diffusion equations with nonlinear convection AIMS Mathematics reaction-diffusion equation nonlinear convection v-shaped traveling front multidimensional stability |
author_facet |
Hui-Ling Niu |
author_sort |
Hui-Ling Niu |
title |
Multidimensional stability of V-shaped traveling fronts in bistable reaction-diffusion equations with nonlinear convection |
title_short |
Multidimensional stability of V-shaped traveling fronts in bistable reaction-diffusion equations with nonlinear convection |
title_full |
Multidimensional stability of V-shaped traveling fronts in bistable reaction-diffusion equations with nonlinear convection |
title_fullStr |
Multidimensional stability of V-shaped traveling fronts in bistable reaction-diffusion equations with nonlinear convection |
title_full_unstemmed |
Multidimensional stability of V-shaped traveling fronts in bistable reaction-diffusion equations with nonlinear convection |
title_sort |
multidimensional stability of v-shaped traveling fronts in bistable reaction-diffusion equations with nonlinear convection |
publisher |
AIMS Press |
series |
AIMS Mathematics |
issn |
2473-6988 |
publishDate |
2021-10-01 |
description |
This paper is concerned with the multidimensional stability of V-shaped traveling fronts for a reaction-diffusion equation with nonlinear convection term in $\mathbb{R}^n$ ($n\geq3$). We consider two cases for initial perturbations: one is that the initial perturbations decay at space infinity and another one is that the initial perturbations do not necessarily decay at space infinity. In the first case, we show that the V-shaped traveling fronts are asymptotically stable. In the second case, we first show that the V-shaped traveling fronts are also asymptotically stable under some further assumptions. At the same time, we also show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which means that the traveling fronts are not asymptotically stable under general bounded perturbations. |
topic |
reaction-diffusion equation nonlinear convection v-shaped traveling front multidimensional stability |
url |
https://www.aimspress.com/article/10.3934/math.2021020/fulltext.html |
work_keys_str_mv |
AT huilingniu multidimensionalstabilityofvshapedtravelingfrontsinbistablereactiondiffusionequationswithnonlinearconvection |
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1724513700002398208 |