Anisotropic parabolic equations with variable nonlinearity

We study the Dirichlet problem for a class of nonlinear parabolic equations with nonstandard anisotropic growth conditions. Equations of this class generalize the evolutional p(x, t)-Laplacian. We prove theorems of existence and uniqueness of weak solutions in suitable Orlicz-Sobolev spaces, derive...

Descripción completa

Detalles Bibliográficos
Autores: Antontsev, S., Shmarev, S.
Tipo de recurso: artículo
Fecha de publicación:2009
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:49671
Acceso en línea:https://ddd.uab.cat/record/49671
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_53209_04
Access Level:acceso abierto
Palabra clave:Nonlinear parabolic equation
Nonstandard growth conditions
Anisotropic nonlinearity
Descripción
Sumario:We study the Dirichlet problem for a class of nonlinear parabolic equations with nonstandard anisotropic growth conditions. Equations of this class generalize the evolutional p(x, t)-Laplacian. We prove theorems of existence and uniqueness of weak solutions in suitable Orlicz-Sobolev spaces, derive global and local in time L∞ bounds for the weak solutions.