Blow up pro les for a quasilinear reaction-diffusion equation with weighted reaction with linear growth

We study the blow up profiles associated to the following second order reaction–diffusion equation with non-homogeneous reaction: ∂tu=∂xx(um)+|x|σu,with σ> 0. Through this study, we show that the non-homogeneous coefficient | x| σ has a strong influence on the blow up behavior of the solutions. F...

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Detalles Bibliográficos
Autores: Sanchez, Ariel, Iagar, Razvan Gabriel
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universidad Rey Juan Carlos
Repositorio:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
OAI Identifier:oai:burjcdigital.urjc.es:10115/29837
Acceso en línea:https://hdl.handle.net/10115/29837
Access Level:acceso abierto
Palabra clave:reaction-di usion equations
non-homogeneous reaction
blow up
critical case
self-similar solutions
phase space analysis
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spelling Blow up pro les for a quasilinear reaction-diffusion equation with weighted reaction with linear growthSanchez, ArielIagar, Razvan Gabrielreaction-di usion equationsnon-homogeneous reactionblow upcritical caseself-similar solutionsphase space analysisWe study the blow up profiles associated to the following second order reaction–diffusion equation with non-homogeneous reaction: ∂tu=∂xx(um)+|x|σu,with σ> 0. Through this study, we show that the non-homogeneous coefficient | x| σ has a strong influence on the blow up behavior of the solutions. First of all, it follows that finite time blow up occurs for self-similar solutions u, a feature that does not appear in the well known autonomous case σ= 0. Moreover, we show that there are three different types of blow up self-similar profiles, depending on whether the exponent σ is closer to zero or not. We also find an explicit blow up profile. The results show in particular that global blow up occurs when σ> 0 is sufficiently small, while for σ> 0 sufficiently large blow up occurs only at infinity, and we give prototypes of these phenomena in form of self-similar solutions with precise behavior. This work is a part of a larger program of understanding the influence of non-homogeneous weights on the blow up sets and rates. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.Springer202420242019info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10115/29837reponame:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlosinstname:Universidad Rey Juan CarlosInglésAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:burjcdigital.urjc.es:10115/298372026-06-24T12:48:17Z
dc.title.none.fl_str_mv Blow up pro les for a quasilinear reaction-diffusion equation with weighted reaction with linear growth
title Blow up pro les for a quasilinear reaction-diffusion equation with weighted reaction with linear growth
spellingShingle Blow up pro les for a quasilinear reaction-diffusion equation with weighted reaction with linear growth
Sanchez, Ariel
reaction-di usion equations
non-homogeneous reaction
blow up
critical case
self-similar solutions
phase space analysis
title_short Blow up pro les for a quasilinear reaction-diffusion equation with weighted reaction with linear growth
title_full Blow up pro les for a quasilinear reaction-diffusion equation with weighted reaction with linear growth
title_fullStr Blow up pro les for a quasilinear reaction-diffusion equation with weighted reaction with linear growth
title_full_unstemmed Blow up pro les for a quasilinear reaction-diffusion equation with weighted reaction with linear growth
title_sort Blow up pro les for a quasilinear reaction-diffusion equation with weighted reaction with linear growth
dc.creator.none.fl_str_mv Sanchez, Ariel
Iagar, Razvan Gabriel
author Sanchez, Ariel
author_facet Sanchez, Ariel
Iagar, Razvan Gabriel
author_role author
author2 Iagar, Razvan Gabriel
author2_role author
dc.subject.none.fl_str_mv reaction-di usion equations
non-homogeneous reaction
blow up
critical case
self-similar solutions
phase space analysis
topic reaction-di usion equations
non-homogeneous reaction
blow up
critical case
self-similar solutions
phase space analysis
description We study the blow up profiles associated to the following second order reaction–diffusion equation with non-homogeneous reaction: ∂tu=∂xx(um)+|x|σu,with σ> 0. Through this study, we show that the non-homogeneous coefficient | x| σ has a strong influence on the blow up behavior of the solutions. First of all, it follows that finite time blow up occurs for self-similar solutions u, a feature that does not appear in the well known autonomous case σ= 0. Moreover, we show that there are three different types of blow up self-similar profiles, depending on whether the exponent σ is closer to zero or not. We also find an explicit blow up profile. The results show in particular that global blow up occurs when σ> 0 is sufficiently small, while for σ> 0 sufficiently large blow up occurs only at infinity, and we give prototypes of these phenomena in form of self-similar solutions with precise behavior. This work is a part of a larger program of understanding the influence of non-homogeneous weights on the blow up sets and rates. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
publishDate 2019
dc.date.none.fl_str_mv 2019
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10115/29837
url https://hdl.handle.net/10115/29837
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
instname:Universidad Rey Juan Carlos
instname_str Universidad Rey Juan Carlos
reponame_str BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
collection BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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