Non-local Diffusion Equations Involving the Fractional p(·) -Laplacian
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/s10884-019-09745-2 http://hdl.handle.net/11449/188971 |
Resumo: | In this paper we study a class of nonlinear quasi-linear diffusion equations involving the fractional p(·) -Laplacian with variable exponents, which is a fractional version of the nonhomogeneous p(·) -Laplace operator. The paper is divided into two parts. In the first part, under suitable conditions on the nonlinearity f, we analyze the problem (P 1 ) in a bounded domain Ω of R N and we establish the well-posedness of solutions by using techniques of monotone operators. We also study the large-time behaviour and extinction of solutions and we prove that the fractional p(·) -Laplacian operator generates a (nonlinear) submarkovian semigroup on L 2 (Ω). In the second part of the paper we establish the existence of global attractors for problem (P 2 ) under certain conditions in the potential V. Our results are new in the literature, both for the case of variable exponents and for the fractional p-laplacian case with constant exponent. |
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Repositório Institucional da UNESP |
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Non-local Diffusion Equations Involving the Fractional p(·) -LaplacianAsymptotic behavior of solutionsAttractorsDiffusion equationsFractional p(x)-Laplace operatorIn this paper we study a class of nonlinear quasi-linear diffusion equations involving the fractional p(·) -Laplacian with variable exponents, which is a fractional version of the nonhomogeneous p(·) -Laplace operator. The paper is divided into two parts. In the first part, under suitable conditions on the nonlinearity f, we analyze the problem (P 1 ) in a bounded domain Ω of R N and we establish the well-posedness of solutions by using techniques of monotone operators. We also study the large-time behaviour and extinction of solutions and we prove that the fractional p(·) -Laplacian operator generates a (nonlinear) submarkovian semigroup on L 2 (Ω). In the second part of the paper we establish the existence of global attractors for problem (P 2 ) under certain conditions in the potential V. Our results are new in the literature, both for the case of variable exponents and for the fractional p-laplacian case with constant exponent.Departamento de Matemática e Computação Faculdade de Ciências e Tecnologia UNESP - Universidade Estadual PaulistaDepartamento de Matemática e Computação Faculdade de Ciências e Tecnologia UNESP - Universidade Estadual PaulistaUniversidade Estadual Paulista (Unesp)Hurtado, Elard J. [UNESP]2019-10-06T16:25:38Z2019-10-06T16:25:38Z2019-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1007/s10884-019-09745-2Journal of Dynamics and Differential Equations.1572-92221040-7294http://hdl.handle.net/11449/18897110.1007/s10884-019-09745-22-s2.0-85064243386Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Dynamics and Differential Equationsinfo:eu-repo/semantics/openAccess2024-06-19T14:31:53Zoai:repositorio.unesp.br:11449/188971Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T17:01:44.582597Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Non-local Diffusion Equations Involving the Fractional p(·) -Laplacian |
title |
Non-local Diffusion Equations Involving the Fractional p(·) -Laplacian |
spellingShingle |
Non-local Diffusion Equations Involving the Fractional p(·) -Laplacian Hurtado, Elard J. [UNESP] Asymptotic behavior of solutions Attractors Diffusion equations Fractional p(x)-Laplace operator |
title_short |
Non-local Diffusion Equations Involving the Fractional p(·) -Laplacian |
title_full |
Non-local Diffusion Equations Involving the Fractional p(·) -Laplacian |
title_fullStr |
Non-local Diffusion Equations Involving the Fractional p(·) -Laplacian |
title_full_unstemmed |
Non-local Diffusion Equations Involving the Fractional p(·) -Laplacian |
title_sort |
Non-local Diffusion Equations Involving the Fractional p(·) -Laplacian |
author |
Hurtado, Elard J. [UNESP] |
author_facet |
Hurtado, Elard J. [UNESP] |
author_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Hurtado, Elard J. [UNESP] |
dc.subject.por.fl_str_mv |
Asymptotic behavior of solutions Attractors Diffusion equations Fractional p(x)-Laplace operator |
topic |
Asymptotic behavior of solutions Attractors Diffusion equations Fractional p(x)-Laplace operator |
description |
In this paper we study a class of nonlinear quasi-linear diffusion equations involving the fractional p(·) -Laplacian with variable exponents, which is a fractional version of the nonhomogeneous p(·) -Laplace operator. The paper is divided into two parts. In the first part, under suitable conditions on the nonlinearity f, we analyze the problem (P 1 ) in a bounded domain Ω of R N and we establish the well-posedness of solutions by using techniques of monotone operators. We also study the large-time behaviour and extinction of solutions and we prove that the fractional p(·) -Laplacian operator generates a (nonlinear) submarkovian semigroup on L 2 (Ω). In the second part of the paper we establish the existence of global attractors for problem (P 2 ) under certain conditions in the potential V. Our results are new in the literature, both for the case of variable exponents and for the fractional p-laplacian case with constant exponent. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-10-06T16:25:38Z 2019-10-06T16:25:38Z 2019-01-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1007/s10884-019-09745-2 Journal of Dynamics and Differential Equations. 1572-9222 1040-7294 http://hdl.handle.net/11449/188971 10.1007/s10884-019-09745-2 2-s2.0-85064243386 |
url |
http://dx.doi.org/10.1007/s10884-019-09745-2 http://hdl.handle.net/11449/188971 |
identifier_str_mv |
Journal of Dynamics and Differential Equations. 1572-9222 1040-7294 10.1007/s10884-019-09745-2 2-s2.0-85064243386 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal of Dynamics and Differential Equations |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808128741864374272 |