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Anisotropic Parabolic Equations with Variable Nonlinearity

S. Antontsev and S. Shmarev

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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.

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Publ. Mat., Volume 53, Number 2 (2009), 355-399.

First available in Project Euclid: 20 July 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations 35K65: Degenerate parabolic equations

Nonlinear parabolic equation nonstandard growth conditions anisotropic nonlinearity


Antontsev, S.; Shmarev, S. Anisotropic Parabolic Equations with Variable Nonlinearity. Publ. Mat. 53 (2009), no. 2, 355--399.

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