Blow-up with logarithmic nonlinearities

We study the asymptotic behaviour of nonnegative solutions of the nonlinear diffusion equation in the half-line with a nonlinear boundary condition, ut = uxx − _(u + 1) logp(u + 1) (x, t) € R+ × (0, T),−ux(0, t) = (u + 1) logq(u + 1)(0, t) t € (0, T),u(x, 0) = u0(x) x € R+, with p, q, _ > 0. We d...

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Detalles Bibliográficos
Autores: Ferreira de Pablo, Raúl, Pablo, Arturo de, Rossi, Julio D.
Tipo de recurso: artículo
Fecha de publicación:2007
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/49646
Acceso en línea:https://hdl.handle.net/20.500.14352/49646
Access Level:acceso abierto
Palabra clave:517.9
Blow-up
Asymptotic behaviour
Nonlinear boundary conditions
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
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spelling Blow-up with logarithmic nonlinearitiesFerreira de Pablo, RaúlPablo, Arturo deRossi, Julio D.517.9Blow-upAsymptotic behaviourNonlinear boundary conditionsEcuaciones diferenciales1202.07 Ecuaciones en DiferenciasWe study the asymptotic behaviour of nonnegative solutions of the nonlinear diffusion equation in the half-line with a nonlinear boundary condition, ut = uxx − _(u + 1) logp(u + 1) (x, t) € R+ × (0, T),−ux(0, t) = (u + 1) logq(u + 1)(0, t) t € (0, T),u(x, 0) = u0(x) x € R+, with p, q, _ > 0. We describe in terms of p, q and when the solution is global in time and when it blows up in finite time. For blow-up solutions we find the blow-up rate and the blow-up set and we describe the asymptotic behaviour close to the blow-up time, showing that a phenomenon of asymptotic simplification takes place. We finally study the appearance of extinction in finite time.ElsevierUniversidad Complutense de Madrid20072007-09-0120072007-09-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/49646reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/496462026-06-02T12:44:21Z
dc.title.none.fl_str_mv Blow-up with logarithmic nonlinearities
title Blow-up with logarithmic nonlinearities
spellingShingle Blow-up with logarithmic nonlinearities
Ferreira de Pablo, Raúl
517.9
Blow-up
Asymptotic behaviour
Nonlinear boundary conditions
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
title_short Blow-up with logarithmic nonlinearities
title_full Blow-up with logarithmic nonlinearities
title_fullStr Blow-up with logarithmic nonlinearities
title_full_unstemmed Blow-up with logarithmic nonlinearities
title_sort Blow-up with logarithmic nonlinearities
dc.creator.none.fl_str_mv Ferreira de Pablo, Raúl
Pablo, Arturo de
Rossi, Julio D.
author Ferreira de Pablo, Raúl
author_facet Ferreira de Pablo, Raúl
Pablo, Arturo de
Rossi, Julio D.
author_role author
author2 Pablo, Arturo de
Rossi, Julio D.
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517.9
Blow-up
Asymptotic behaviour
Nonlinear boundary conditions
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
topic 517.9
Blow-up
Asymptotic behaviour
Nonlinear boundary conditions
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
description We study the asymptotic behaviour of nonnegative solutions of the nonlinear diffusion equation in the half-line with a nonlinear boundary condition, ut = uxx − _(u + 1) logp(u + 1) (x, t) € R+ × (0, T),−ux(0, t) = (u + 1) logq(u + 1)(0, t) t € (0, T),u(x, 0) = u0(x) x € R+, with p, q, _ > 0. We describe in terms of p, q and when the solution is global in time and when it blows up in finite time. For blow-up solutions we find the blow-up rate and the blow-up set and we describe the asymptotic behaviour close to the blow-up time, showing that a phenomenon of asymptotic simplification takes place. We finally study the appearance of extinction in finite time.
publishDate 2007
dc.date.none.fl_str_mv 2007
2007-09-01
2007
2007-09-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/49646
url https://hdl.handle.net/20.500.14352/49646
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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