Non-local Diffusion Equations Involving the Fractional p(·) -Laplacian
dc.contributor.author | Hurtado, Elard J. [UNESP] | |
dc.contributor.institution | Universidade Estadual Paulista (Unesp) | |
dc.date.accessioned | 2019-10-06T16:25:38Z | |
dc.date.available | 2019-10-06T16:25:38Z | |
dc.date.issued | 2019-01-01 | |
dc.description.abstract | 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. | en |
dc.description.affiliation | Departamento de Matemática e Computação Faculdade de Ciências e Tecnologia UNESP - Universidade Estadual Paulista | |
dc.description.affiliationUnesp | Departamento de Matemática e Computação Faculdade de Ciências e Tecnologia UNESP - Universidade Estadual Paulista | |
dc.identifier | http://dx.doi.org/10.1007/s10884-019-09745-2 | |
dc.identifier.citation | Journal of Dynamics and Differential Equations. | |
dc.identifier.doi | 10.1007/s10884-019-09745-2 | |
dc.identifier.issn | 1572-9222 | |
dc.identifier.issn | 1040-7294 | |
dc.identifier.scopus | 2-s2.0-85064243386 | |
dc.identifier.uri | http://hdl.handle.net/11449/188971 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Dynamics and Differential Equations | |
dc.rights.accessRights | Acesso aberto | |
dc.source | Scopus | |
dc.subject | Asymptotic behavior of solutions | |
dc.subject | Attractors | |
dc.subject | Diffusion equations | |
dc.subject | Fractional p(x)-Laplace operator | |
dc.title | Non-local Diffusion Equations Involving the Fractional p(·) -Laplacian | en |
dc.type | Artigo | |
unesp.author.orcid | 0000-0002-6799-8253[1] | |
unesp.department | Matemática e Computação - FCT | pt |