Self-similar solutions preventing finite time blow-up for reaction-diffusion equations with singular potential

We prove existence and uniqueness of a global in time self-similar solution growing up as t → ∞ for the following reaction-diffusion equation with a singular potential ∂tu = ∆u^m + |x|^σ u^p posed in dimension N ≥ 2, with m > 1, σ ∈ (−2, 0) and 1 <p< 1 − σ (m − 1)/2. For the special case of...

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Detalles Bibliográficos
Autores: Iagar, Razvan Gabriel, Muñoz Montalvo, Ana Isabel, Sánchez, Ariel
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad Rey Juan Carlos
Repositorio:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
OAI Identifier:oai:burjcdigital.urjc.es:10115/26801
Acceso en línea:https://hdl.handle.net/10115/26801
Access Level:acceso abierto
Palabra clave:Reaction-diffusion equations
Non-uniqueness
Global solutions
Singular potential
Hardy-type equations
Self-similar solutions.
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spelling Self-similar solutions preventing finite time blow-up for reaction-diffusion equations with singular potentialIagar, Razvan GabrielMuñoz Montalvo, Ana IsabelSánchez, ArielReaction-diffusion equationsNon-uniquenessGlobal solutionsSingular potentialHardy-type equationsSelf-similar solutions.We prove existence and uniqueness of a global in time self-similar solution growing up as t → ∞ for the following reaction-diffusion equation with a singular potential ∂tu = ∆u^m + |x|^σ u^p posed in dimension N ≥ 2, with m > 1, σ ∈ (−2, 0) and 1 <p< 1 − σ (m − 1)/2. For the special case of dimension N = 1, the same holds true for σ ∈ (−1, 0) and similar ranges for m and p. The existence of this global solution prevents finite time blow-up even with m > 1 and p > 1, showing an interesting effect induced by the singular potential |x|^σ . This result is also applied to reaction-diffusion equations with general potentials V (x) to prevent finite time blow-up via comparison.202320232023info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10115/26801reponame:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlosinstname:Universidad Rey Juan CarlosInglésAttribution-NonCommercial-NoDerivs 4.0 Internationalhttps://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:burjcdigital.urjc.es:10115/268012026-06-24T12:48:17Z
dc.title.none.fl_str_mv Self-similar solutions preventing finite time blow-up for reaction-diffusion equations with singular potential
title Self-similar solutions preventing finite time blow-up for reaction-diffusion equations with singular potential
spellingShingle Self-similar solutions preventing finite time blow-up for reaction-diffusion equations with singular potential
Iagar, Razvan Gabriel
Reaction-diffusion equations
Non-uniqueness
Global solutions
Singular potential
Hardy-type equations
Self-similar solutions.
title_short Self-similar solutions preventing finite time blow-up for reaction-diffusion equations with singular potential
title_full Self-similar solutions preventing finite time blow-up for reaction-diffusion equations with singular potential
title_fullStr Self-similar solutions preventing finite time blow-up for reaction-diffusion equations with singular potential
title_full_unstemmed Self-similar solutions preventing finite time blow-up for reaction-diffusion equations with singular potential
title_sort Self-similar solutions preventing finite time blow-up for reaction-diffusion equations with singular potential
dc.creator.none.fl_str_mv Iagar, Razvan Gabriel
Muñoz Montalvo, Ana Isabel
Sánchez, Ariel
author Iagar, Razvan Gabriel
author_facet Iagar, Razvan Gabriel
Muñoz Montalvo, Ana Isabel
Sánchez, Ariel
author_role author
author2 Muñoz Montalvo, Ana Isabel
Sánchez, Ariel
author2_role author
author
dc.subject.none.fl_str_mv Reaction-diffusion equations
Non-uniqueness
Global solutions
Singular potential
Hardy-type equations
Self-similar solutions.
topic Reaction-diffusion equations
Non-uniqueness
Global solutions
Singular potential
Hardy-type equations
Self-similar solutions.
description We prove existence and uniqueness of a global in time self-similar solution growing up as t → ∞ for the following reaction-diffusion equation with a singular potential ∂tu = ∆u^m + |x|^σ u^p posed in dimension N ≥ 2, with m > 1, σ ∈ (−2, 0) and 1 <p< 1 − σ (m − 1)/2. For the special case of dimension N = 1, the same holds true for σ ∈ (−1, 0) and similar ranges for m and p. The existence of this global solution prevents finite time blow-up even with m > 1 and p > 1, showing an interesting effect induced by the singular potential |x|^σ . This result is also applied to reaction-diffusion equations with general potentials V (x) to prevent finite time blow-up via comparison.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023
2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10115/26801
url https://hdl.handle.net/10115/26801
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv Attribution-NonCommercial-NoDerivs 4.0 International
https://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivs 4.0 International
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
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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