Growing solutions of the fractional p-Laplacian equation in the Fast Diffusion range

We establish existence, uniqueness as well as quantitative estimates for solutions u(t,x) to the fractional nonlinear diffusion equation, ∂tu+Ls,p(u) = 0, where Ls,p= (−Δ)sp is the standard fractional p-Laplacian operator. We work in the range of exponents 0 < s < 1 and 1 < p < 2, and in...

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Detalhes bibliográficos
Autor: Vázquez Suárez, Juan Luis
Formato: artículo
Fecha de publicación:2022
País:España
Recursos:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/700583
Acesso em linha:http://hdl.handle.net/10486/700583
https://dx.doi.org/10.1016/j.na.2021.112575
Access Level:acceso abierto
Palavra-chave:Extinction
Fractional operators
Nonlinear parabolic equations
p-Laplacian operator
Self-similar solutions
Solutions with growing data
Matemáticas
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spelling Growing solutions of the fractional p-Laplacian equation in the Fast Diffusion rangeVázquez Suárez, Juan LuisExtinctionFractional operatorsNonlinear parabolic equationsp-Laplacian operatorSelf-similar solutionsSolutions with growing dataMatemáticasWe establish existence, uniqueness as well as quantitative estimates for solutions u(t,x) to the fractional nonlinear diffusion equation, ∂tu+Ls,p(u) = 0, where Ls,p= (−Δ)sp is the standard fractional p-Laplacian operator. We work in the range of exponents 0 < s < 1 and 1 < p < 2, and in some sections we need sp <1. The equation is posed in the whole space x ∈ RN. We first obtain weighted global integral estimates that allow establishing the existence of solutions for a class of large data that is proved to be roughly optimal. We use the estimates to study the class of self-similar solutions of forward type, that we describe in detail when they exist. We also explain what happens when possible self-similar solutions do not exist. We establish the dichotomy positivity versus extinction for nonnegative solutions at any given time. We analyse the conditions for extinction in finite timeAuthor partially funded by Project PGC2018-098440-B-I00 (Spain)ElsevierDepartamento de MatemáticasFacultad de Ciencias20222022-01-01research articlehttp://purl.org/coar/resource_type/c_2df8fbb1VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/700583https://dx.doi.org/10.1016/j.na.2021.112575reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/7005832026-06-23T12:46:27Z
dc.title.none.fl_str_mv Growing solutions of the fractional p-Laplacian equation in the Fast Diffusion range
title Growing solutions of the fractional p-Laplacian equation in the Fast Diffusion range
spellingShingle Growing solutions of the fractional p-Laplacian equation in the Fast Diffusion range
Vázquez Suárez, Juan Luis
Extinction
Fractional operators
Nonlinear parabolic equations
p-Laplacian operator
Self-similar solutions
Solutions with growing data
Matemáticas
title_short Growing solutions of the fractional p-Laplacian equation in the Fast Diffusion range
title_full Growing solutions of the fractional p-Laplacian equation in the Fast Diffusion range
title_fullStr Growing solutions of the fractional p-Laplacian equation in the Fast Diffusion range
title_full_unstemmed Growing solutions of the fractional p-Laplacian equation in the Fast Diffusion range
title_sort Growing solutions of the fractional p-Laplacian equation in the Fast Diffusion range
dc.creator.none.fl_str_mv Vázquez Suárez, Juan Luis
author Vázquez Suárez, Juan Luis
author_facet Vázquez Suárez, Juan Luis
author_role author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv Extinction
Fractional operators
Nonlinear parabolic equations
p-Laplacian operator
Self-similar solutions
Solutions with growing data
Matemáticas
topic Extinction
Fractional operators
Nonlinear parabolic equations
p-Laplacian operator
Self-similar solutions
Solutions with growing data
Matemáticas
description We establish existence, uniqueness as well as quantitative estimates for solutions u(t,x) to the fractional nonlinear diffusion equation, ∂tu+Ls,p(u) = 0, where Ls,p= (−Δ)sp is the standard fractional p-Laplacian operator. We work in the range of exponents 0 < s < 1 and 1 < p < 2, and in some sections we need sp <1. The equation is posed in the whole space x ∈ RN. We first obtain weighted global integral estimates that allow establishing the existence of solutions for a class of large data that is proved to be roughly optimal. We use the estimates to study the class of self-similar solutions of forward type, that we describe in detail when they exist. We also explain what happens when possible self-similar solutions do not exist. We establish the dichotomy positivity versus extinction for nonnegative solutions at any given time. We analyse the conditions for extinction in finite time
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-01-01
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10486/700583
https://dx.doi.org/10.1016/j.na.2021.112575
url http://hdl.handle.net/10486/700583
https://dx.doi.org/10.1016/j.na.2021.112575
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:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
collection Biblos-e Archivo. Repositorio Institucional de la UAM
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,198674

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