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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Published inAIMS mathematics Vol. 6; no. 1; pp. 314 - 332
Main Author Niu, Hui-Ling
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
multidimensional stability
nonlinear convection
reaction-diffusion equation
v-shaped traveling front
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ISSN2473-6988
2473-6988
DOI10.3934/math.2021020

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Abstract 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.
AbstractList 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.
Author Niu, Hui-Ling
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Cites_doi 10.1007/978-3-642-61798-0
10.1016/j.jde.2015.12.045
10.3934/dcdss.2011.4.101
10.1016/j.nonrwa.2018.10.005
10.1016/j.jde.2011.08.029
10.1016/j.jde.2004.06.011
10.1007/s00028-017-0397-z
10.3934/dcds.2012.32.1011
10.3934/dcds.2006.14.203
10.1080/03605309208820907
10.3934/dcdsb.2015.20.1015
10.57262/die/1356019308
10.1007/978-3-0348-9234-6
10.1017/S0308210515000268
10.1007/s11425-016-0015-x
10.3934/dcdsb.2017055
10.1080/03605300902963500
10.1007/978-3-0348-7964-4
10.1080/03605300008821532
10.1007/s10884-019-09779-6
10.1080/03605309208820908
10.1007/PL00004238
10.1137/060661788
10.1186/s13662-019-2438-0
10.57262/ade/1355926855
10.1016/j.ansens.2004.03.001
10.1016/j.jde.2011.01.017
10.1016/j.jde.2012.04.022
10.12775/TMNA.1998.002
10.57262/die/1356019305
10.1016/j.nonrwa.2018.10.003
10.1007/s11425-013-4699-5
10.1016/j.na.2020.111791
10.1016/j.jde.2011.09.016
10.3934/dcds.2006.14.75
10.12775/TMNA.2000.029
10.1016/j.aim.2015.11.033
10.1016/j.jde.2008.06.037
10.1007/s10231-008-0072-7
10.1016/j.jde.2018.01.020
10.3934/dcds.2006.15.819
10.3934/dcds.2005.13.1069
10.1090/S0002-9947-97-01668-1
10.1016/j.aml.2020.106509
10.1137/S0036141097316391
10.1515/anona-2020-0127
10.3934/dcds.2012.32.2339
10.57262/die/1356039441
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References key-10.3934/math.2021020-1
key-10.3934/math.2021020-47
key-10.3934/math.2021020-2
key-10.3934/math.2021020-48
key-10.3934/math.2021020-45
key-10.3934/math.2021020-46
key-10.3934/math.2021020-43
key-10.3934/math.2021020-44
key-10.3934/math.2021020-41
key-10.3934/math.2021020-42
key-10.3934/math.2021020-9
key-10.3934/math.2021020-40
key-10.3934/math.2021020-7
key-10.3934/math.2021020-8
key-10.3934/math.2021020-5
key-10.3934/math.2021020-6
key-10.3934/math.2021020-3
key-10.3934/math.2021020-4
key-10.3934/math.2021020-38
key-10.3934/math.2021020-39
key-10.3934/math.2021020-14
key-10.3934/math.2021020-15
key-10.3934/math.2021020-12
key-10.3934/math.2021020-13
key-10.3934/math.2021020-10
key-10.3934/math.2021020-11
key-10.3934/math.2021020-49
key-10.3934/math.2021020-25
key-10.3934/math.2021020-26
key-10.3934/math.2021020-23
key-10.3934/math.2021020-24
key-10.3934/math.2021020-21
key-10.3934/math.2021020-22
key-10.3934/math.2021020-20
key-10.3934/math.2021020-18
key-10.3934/math.2021020-19
key-10.3934/math.2021020-16
key-10.3934/math.2021020-17
key-10.3934/math.2021020-36
key-10.3934/math.2021020-37
key-10.3934/math.2021020-34
key-10.3934/math.2021020-35
key-10.3934/math.2021020-32
key-10.3934/math.2021020-33
key-10.3934/math.2021020-30
key-10.3934/math.2021020-31
key-10.3934/math.2021020-29
key-10.3934/math.2021020-27
key-10.3934/math.2021020-28
References_xml – ident: key-10.3934/math.2021020-48
  doi: 10.1007/978-3-642-61798-0
– ident: key-10.3934/math.2021020-37
  doi: 10.1016/j.jde.2015.12.045
– ident: key-10.3934/math.2021020-19
  doi: 10.3934/dcdss.2011.4.101
– ident: key-10.3934/math.2021020-35
  doi: 10.1016/j.nonrwa.2018.10.005
– ident: key-10.3934/math.2021020-41
  doi: 10.1016/j.jde.2011.08.029
– ident: key-10.3934/math.2021020-11
  doi: 10.1016/j.jde.2004.06.011
– ident: key-10.3934/math.2021020-38
  doi: 10.1007/s00028-017-0397-z
– ident: key-10.3934/math.2021020-25
  doi: 10.3934/dcds.2012.32.1011
– ident: key-10.3934/math.2021020-47
  doi: 10.3934/dcds.2006.14.203
– ident: key-10.3934/math.2021020-43
  doi: 10.1080/03605309208820907
– ident: key-10.3934/math.2021020-45
  doi: 10.3934/dcdsb.2015.20.1015
– ident: key-10.3934/math.2021020-4
  doi: 10.57262/die/1356019308
– ident: key-10.3934/math.2021020-46
  doi: 10.1007/978-3-0348-9234-6
– ident: key-10.3934/math.2021020-30
  doi: 10.1017/S0308210515000268
– ident: key-10.3934/math.2021020-31
  doi: 10.1007/s11425-016-0015-x
– ident: key-10.3934/math.2021020-32
  doi: 10.3934/dcdsb.2017055
– ident: key-10.3934/math.2021020-42
  doi: 10.1080/03605300902963500
– ident: key-10.3934/math.2021020-8
  doi: 10.1007/978-3-0348-7964-4
– ident: key-10.3934/math.2021020-14
  doi: 10.1080/03605300008821532
– ident: key-10.3934/math.2021020-22
  doi: 10.1007/s10884-019-09779-6
– ident: key-10.3934/math.2021020-40
  doi: 10.1080/03605309208820908
– ident: key-10.3934/math.2021020-18
  doi: 10.1007/PL00004238
– ident: key-10.3934/math.2021020-23
  doi: 10.1137/060661788
– ident: key-10.3934/math.2021020-10
  doi: 10.1186/s13662-019-2438-0
– ident: key-10.3934/math.2021020-3
  doi: 10.57262/ade/1355926855
– ident: key-10.3934/math.2021020-17
  doi: 10.1016/j.ansens.2004.03.001
– ident: key-10.3934/math.2021020-33
  doi: 10.1016/j.jde.2011.01.017
– ident: key-10.3934/math.2021020-6
  doi: 10.1016/j.jde.2012.04.022
– ident: key-10.3934/math.2021020-1
  doi: 10.12775/TMNA.1998.002
– ident: key-10.3934/math.2021020-7
  doi: 10.57262/die/1356019305
– ident: key-10.3934/math.2021020-26
  doi: 10.1016/j.nonrwa.2018.10.003
– ident: key-10.3934/math.2021020-28
  doi: 10.1007/s11425-013-4699-5
– ident: key-10.3934/math.2021020-34
  doi: 10.1016/j.na.2020.111791
– ident: key-10.3934/math.2021020-21
  doi: 10.1016/j.jde.2011.09.016
– ident: key-10.3934/math.2021020-16
  doi: 10.3934/dcds.2006.14.75
– ident: key-10.3934/math.2021020-2
  doi: 10.12775/TMNA.2000.029
– ident: key-10.3934/math.2021020-13
  doi: 10.1016/j.aim.2015.11.033
– ident: key-10.3934/math.2021020-24
  doi: 10.1016/j.jde.2008.06.037
– ident: key-10.3934/math.2021020-44
  doi: 10.1007/s10231-008-0072-7
– ident: key-10.3934/math.2021020-27
  doi: 10.1016/j.jde.2018.01.020
– ident: key-10.3934/math.2021020-49
– ident: key-10.3934/math.2021020-20
  doi: 10.3934/dcds.2006.15.819
– ident: key-10.3934/math.2021020-15
  doi: 10.3934/dcds.2005.13.1069
– ident: key-10.3934/math.2021020-39
  doi: 10.1090/S0002-9947-97-01668-1
– ident: key-10.3934/math.2021020-36
  doi: 10.1016/j.aml.2020.106509
– ident: key-10.3934/math.2021020-12
  doi: 10.1137/S0036141097316391
– ident: key-10.3934/math.2021020-9
  doi: 10.1515/anona-2020-0127
– ident: key-10.3934/math.2021020-29
  doi: 10.3934/dcds.2012.32.2339
– ident: key-10.3934/math.2021020-5
  doi: 10.57262/die/1356039441
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SubjectTerms multidimensional stability
nonlinear convection
reaction-diffusion equation
v-shaped traveling front
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Title Multidimensional stability of V-shaped traveling fronts in bistable reaction-diffusion equations with nonlinear convection
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