Travelling wave profiles in some models with nonlinear diffusion
Autor(a) principal: | |
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Data de Publicação: | 2014 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.21/5018 |
Resumo: | We study some properties of the monotone solutions of the boundary value problem (p(u'))' - cu' + f(u) = 0, u(-infinity) = 0, u(+infinity) = 1, where f is a continuous function, positive in (0, 1) and taking the value zero at 0 and 1, and P may be an increasing homeomorphism of (0, 1) or (0, +infinity) onto [0, +infinity). This problem arises when we look for travelling waves for the reaction diffusion equation partial derivative u/partial derivative t = partial derivative/partial derivative x [p(partial derivative u/partial derivative x)] + f(u) with the parameter c representing the wave speed. A possible model for the nonlinear diffusion is the relativistic curvature operator p(nu)= nu/root 1-nu(2). The same ideas apply when P is given by the one- dimensional p- Laplacian P(v) = |v|(p-2)v. In this case, an advection term is also considered. We show that, as for the classical Fisher- Kolmogorov- Petrovski- Piskounov equations, there is an interval of admissible speeds c and we give characterisations of the critical speed c. We also present some examples of exact solutions. (C) 2014 Elsevier Inc. All rights reserved. |
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Travelling wave profiles in some models with nonlinear diffusionRelativistic Curvaturep-LaplacianFKPP EquationHeteroclinicTravelling WaveCritical SpeedWe study some properties of the monotone solutions of the boundary value problem (p(u'))' - cu' + f(u) = 0, u(-infinity) = 0, u(+infinity) = 1, where f is a continuous function, positive in (0, 1) and taking the value zero at 0 and 1, and P may be an increasing homeomorphism of (0, 1) or (0, +infinity) onto [0, +infinity). This problem arises when we look for travelling waves for the reaction diffusion equation partial derivative u/partial derivative t = partial derivative/partial derivative x [p(partial derivative u/partial derivative x)] + f(u) with the parameter c representing the wave speed. A possible model for the nonlinear diffusion is the relativistic curvature operator p(nu)= nu/root 1-nu(2). The same ideas apply when P is given by the one- dimensional p- Laplacian P(v) = |v|(p-2)v. In this case, an advection term is also considered. We show that, as for the classical Fisher- Kolmogorov- Petrovski- Piskounov equations, there is an interval of admissible speeds c and we give characterisations of the critical speed c. We also present some examples of exact solutions. (C) 2014 Elsevier Inc. All rights reserved.Elsevier Science IncRCIPLCoelho, Maria Isabel EstevesSanchez, Luis2015-08-25T14:55:03Z2014-05-252014-05-25T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/5018engCOELHO, Maria Isabel Esteves; SANCHEZ, Luís – Travelling wave profiles in some models with nonlinear diffusion. Applied Mathematics and Computation. ISSN: 0096-3003. Vol. 235 (2014), pp. 469-4810096-300310.1016/j.amc.2014.02.104metadata only accessinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-08-03T09:47:51Zoai:repositorio.ipl.pt:10400.21/5018Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:14:21.691865Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Travelling wave profiles in some models with nonlinear diffusion |
title |
Travelling wave profiles in some models with nonlinear diffusion |
spellingShingle |
Travelling wave profiles in some models with nonlinear diffusion Coelho, Maria Isabel Esteves Relativistic Curvature p-Laplacian FKPP Equation Heteroclinic Travelling Wave Critical Speed |
title_short |
Travelling wave profiles in some models with nonlinear diffusion |
title_full |
Travelling wave profiles in some models with nonlinear diffusion |
title_fullStr |
Travelling wave profiles in some models with nonlinear diffusion |
title_full_unstemmed |
Travelling wave profiles in some models with nonlinear diffusion |
title_sort |
Travelling wave profiles in some models with nonlinear diffusion |
author |
Coelho, Maria Isabel Esteves |
author_facet |
Coelho, Maria Isabel Esteves Sanchez, Luis |
author_role |
author |
author2 |
Sanchez, Luis |
author2_role |
author |
dc.contributor.none.fl_str_mv |
RCIPL |
dc.contributor.author.fl_str_mv |
Coelho, Maria Isabel Esteves Sanchez, Luis |
dc.subject.por.fl_str_mv |
Relativistic Curvature p-Laplacian FKPP Equation Heteroclinic Travelling Wave Critical Speed |
topic |
Relativistic Curvature p-Laplacian FKPP Equation Heteroclinic Travelling Wave Critical Speed |
description |
We study some properties of the monotone solutions of the boundary value problem (p(u'))' - cu' + f(u) = 0, u(-infinity) = 0, u(+infinity) = 1, where f is a continuous function, positive in (0, 1) and taking the value zero at 0 and 1, and P may be an increasing homeomorphism of (0, 1) or (0, +infinity) onto [0, +infinity). This problem arises when we look for travelling waves for the reaction diffusion equation partial derivative u/partial derivative t = partial derivative/partial derivative x [p(partial derivative u/partial derivative x)] + f(u) with the parameter c representing the wave speed. A possible model for the nonlinear diffusion is the relativistic curvature operator p(nu)= nu/root 1-nu(2). The same ideas apply when P is given by the one- dimensional p- Laplacian P(v) = |v|(p-2)v. In this case, an advection term is also considered. We show that, as for the classical Fisher- Kolmogorov- Petrovski- Piskounov equations, there is an interval of admissible speeds c and we give characterisations of the critical speed c. We also present some examples of exact solutions. (C) 2014 Elsevier Inc. All rights reserved. |
publishDate |
2014 |
dc.date.none.fl_str_mv |
2014-05-25 2014-05-25T00:00:00Z 2015-08-25T14:55:03Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.21/5018 |
url |
http://hdl.handle.net/10400.21/5018 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
COELHO, Maria Isabel Esteves; SANCHEZ, Luís – Travelling wave profiles in some models with nonlinear diffusion. Applied Mathematics and Computation. ISSN: 0096-3003. Vol. 235 (2014), pp. 469-481 0096-3003 10.1016/j.amc.2014.02.104 |
dc.rights.driver.fl_str_mv |
metadata only access info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
metadata only access |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier Science Inc |
publisher.none.fl_str_mv |
Elsevier Science Inc |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799133401582665728 |