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45 p, 316.1 KB Anisotropic parabolic equations with variable nonlinearity / Antontsev, S. (Universidade de Lisboa. Centro de Matemática e Aplicacôes Fundamentais (CMAF)) ; Shmarev, S. (Universidad de Oviedo. Departamento de Matemáticas)
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.
2009 - 10.5565/PUBLMAT_53209_04
Publicacions matemàtiques, V. 53 n. 2 (2009) p. 355-399  

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