Existence of weak solutions to nonlocal PDEs with a generalized definition of Caputo derivative

Some compactness criteria that are analogies of the Aubin–Lions lemma for the existence of weak solutions of nonlinear evolutionary PDEs play crucial roles for the existence of weak solutions to time-fractional PDEs. Based on this fact, in this paper, we consider the existence of weak solutions to a...

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Detalles Bibliográficos
Autores: Xu, Jiaohui, Caraballo Garrido, Tomás
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2022
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/147909
Acceso en línea:https://hdl.handle.net/11441/147909
https://doi.org/10.1007/s00009-023-02429-8
Access Level:acceso abierto
Palabra clave:Time fractional PDEs
Fractional Laplacian operator
Compactness criteria
Descripción
Sumario:Some compactness criteria that are analogies of the Aubin–Lions lemma for the existence of weak solutions of nonlinear evolutionary PDEs play crucial roles for the existence of weak solutions to time-fractional PDEs. Based on this fact, in this paper, we consider the existence of weak solutions to a kind of partial differential equations with Caputo time-fractional differential operator of order γ∈(0,1) and fractional Laplacian operator (−Δ)α , α∈(0,1).