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2009 Anisotropic Parabolic Equations with Variable Nonlinearity
S. Antontsev, S. Shmarev
Publ. Mat. 53(2): 355-399 (2009).

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.

Citation

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S. Antontsev. S. Shmarev. "Anisotropic Parabolic Equations with Variable Nonlinearity." Publ. Mat. 53 (2) 355 - 399, 2009.

Information

Published: 2009
First available in Project Euclid: 20 July 2009

zbMATH: 1191.35152
MathSciNet: MR2543856

Subjects:
Primary: 35K55, 35K65

Rights: Copyright © 2009 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.53 • No. 2 • 2009
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