Instantaneous and finite time blow-up of solutions toareaction-diffusion equation with Hardy-type singular potential

We deal with radially symmetric solutions to the reaction-diffusion equation with Hardy-type singular potential ut = Δum + K |x|2 um, posed in RN × (0, T), in dimension N ≥ 3, where m > 1 and 0 <K< (N − 2)2/4. We prove that, in dependence of the initial condition u0 ∈ L∞(RN ) ∩ C(RN ), its...

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Detalles Bibliográficos
Autores: Sanchez, Ariel, Iagar, Razvan Gabriel
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universidad Rey Juan Carlos
Repositorio:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
OAI Identifier:oai:burjcdigital.urjc.es:10115/29823
Acceso en línea:https://hdl.handle.net/10115/29823
Access Level:acceso abierto
Palabra clave:Reaction-diffusion equations
Hardy-type potential
Instantaneous blow-up
Non-homogeneous porous medium
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spelling Instantaneous and finite time blow-up of solutions toareaction-diffusion equation with Hardy-type singular potentialSanchez, ArielIagar, Razvan GabrielReaction-diffusion equationsHardy-type potentialInstantaneous blow-upNon-homogeneous porous mediumWe deal with radially symmetric solutions to the reaction-diffusion equation with Hardy-type singular potential ut = Δum + K |x|2 um, posed in RN × (0, T), in dimension N ≥ 3, where m > 1 and 0 <K< (N − 2)2/4. We prove that, in dependence of the initial condition u0 ∈ L∞(RN ) ∩ C(RN ), its solutions may either blow up instantaneously or blow up in finite time at the origin, thus developing a singularity at x = 0, but they can be continued globally in weak sense. The instantaneous blow-up occurs for example for any data u0 such that u0(0) > 0. The proofs are based on a transformation mapping solutions to our equation into solutions to a non-homogeneous porous medium equation.Elsevier202420242020info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10115/29823reponame: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:10115/298232026-06-24T12:48:17Z
dc.title.none.fl_str_mv Instantaneous and finite time blow-up of solutions toareaction-diffusion equation with Hardy-type singular potential
title Instantaneous and finite time blow-up of solutions toareaction-diffusion equation with Hardy-type singular potential
spellingShingle Instantaneous and finite time blow-up of solutions toareaction-diffusion equation with Hardy-type singular potential
Sanchez, Ariel
Reaction-diffusion equations
Hardy-type potential
Instantaneous blow-up
Non-homogeneous porous medium
title_short Instantaneous and finite time blow-up of solutions toareaction-diffusion equation with Hardy-type singular potential
title_full Instantaneous and finite time blow-up of solutions toareaction-diffusion equation with Hardy-type singular potential
title_fullStr Instantaneous and finite time blow-up of solutions toareaction-diffusion equation with Hardy-type singular potential
title_full_unstemmed Instantaneous and finite time blow-up of solutions toareaction-diffusion equation with Hardy-type singular potential
title_sort Instantaneous and finite time blow-up of solutions toareaction-diffusion equation with Hardy-type singular potential
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-diffusion equations
Hardy-type potential
Instantaneous blow-up
Non-homogeneous porous medium
topic Reaction-diffusion equations
Hardy-type potential
Instantaneous blow-up
Non-homogeneous porous medium
description We deal with radially symmetric solutions to the reaction-diffusion equation with Hardy-type singular potential ut = Δum + K |x|2 um, posed in RN × (0, T), in dimension N ≥ 3, where m > 1 and 0 <K< (N − 2)2/4. We prove that, in dependence of the initial condition u0 ∈ L∞(RN ) ∩ C(RN ), its solutions may either blow up instantaneously or blow up in finite time at the origin, thus developing a singularity at x = 0, but they can be continued globally in weak sense. The instantaneous blow-up occurs for example for any data u0 such that u0(0) > 0. The proofs are based on a transformation mapping solutions to our equation into solutions to a non-homogeneous porous medium equation.
publishDate 2020
dc.date.none.fl_str_mv 2020
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/10115/29823
url https://hdl.handle.net/10115/29823
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 Elsevier
publisher.none.fl_str_mv Elsevier
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 15,228081

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