Existence and uniqueness for the inhomogeneous 1-Laplace evolution equation revisited

In this paper we deal with an inhomogeneous parabolic Dirichlet problem involving the 1-Laplacian operator. We show the existence of a unique solution when data belong to L^1(0,T;L^2(\Omega)) for every T>0. As a consequence, global existence and uniqueness for data in L^1_{loc}(0,+\infty;L^2(\Ome...

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Detalles Bibliográficos
Autores: Latorre, Marta, Segura de León, Sergio
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad Rey Juan Carlos
Repositorio:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
OAI Identifier:oai:burjcdigital.urjc.es:10115/31915
Acceso en línea:https://hdl.handle.net/10115/31915
Access Level:acceso embargado
Palabra clave:Nonlinear parabolic equations
1-Laplacian operator
Existence
Uniqueness
Descripción
Sumario:In this paper we deal with an inhomogeneous parabolic Dirichlet problem involving the 1-Laplacian operator. We show the existence of a unique solution when data belong to L^1(0,T;L^2(\Omega)) for every T>0. As a consequence, global existence and uniqueness for data in L^1_{loc}(0,+\infty;L^2(\Omega)) is obtained. Our analysis retrieves previous results in a correct and complete way.