Anisotropic Parabolic Equations with Variable Nonlinearity
S. Antontsev and S. Shmarev
Source: Publ. Mat. Volume 53, Number 2 (2009), 355-399.
Abstract
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 $L^{\infty}$ bounds for the weak solutions.
Primary Subjects: 35K55, 35K65
Keywords: Nonlinear parabolic equation; nonstandard growth conditions; anisotropic nonlinearity
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2009 © Universitat Autònoma de Barcelona, Departament de Matemàtiques
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