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Non-local Diffusion Equations Involving the Fractional p(·) -Laplacian

dc.contributor.authorHurtado, Elard J. [UNESP]
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2019-10-06T16:25:38Z
dc.date.available2019-10-06T16:25:38Z
dc.date.issued2019-01-01
dc.description.abstractIn 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.en
dc.description.affiliationDepartamento de Matemática e Computação Faculdade de Ciências e Tecnologia UNESP - Universidade Estadual Paulista
dc.description.affiliationUnespDepartamento de Matemática e Computação Faculdade de Ciências e Tecnologia UNESP - Universidade Estadual Paulista
dc.identifierhttp://dx.doi.org/10.1007/s10884-019-09745-2
dc.identifier.citationJournal of Dynamics and Differential Equations.
dc.identifier.doi10.1007/s10884-019-09745-2
dc.identifier.issn1572-9222
dc.identifier.issn1040-7294
dc.identifier.scopus2-s2.0-85064243386
dc.identifier.urihttp://hdl.handle.net/11449/188971
dc.language.isoeng
dc.relation.ispartofJournal of Dynamics and Differential Equations
dc.rights.accessRightsAcesso aberto
dc.sourceScopus
dc.subjectAsymptotic behavior of solutions
dc.subjectAttractors
dc.subjectDiffusion equations
dc.subjectFractional p(x)-Laplace operator
dc.titleNon-local Diffusion Equations Involving the Fractional p(·) -Laplacianen
dc.typeArtigo
unesp.author.orcid0000-0002-6799-8253[1]
unesp.departmentMatemática e Computação - FCTpt

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