Revistes Catalanes amb Accés Obert (RACO)

Anisotropic parabolic equations with variable nonlinearity

S. Antontsev, S. Shmarev


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.

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