Parabolic Equations with Anisotropic Nonstandard Growth Conditions

S Antontsev,S Shmarev

doi:10.1007/978-3-7643-7719-9_4

Parabolic Equations with Anisotropic Nonstandard Growth Conditions

S Antontsev, S Shmarev

https://doi.org/10.1007/978-3-7643-7719-9_4

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Publication Date: Jan 1, 2006

Citations: 58

Affiliation: University of Beira Interior, University of Oviedo

#Class Of Nonlinear Parabolic Equations #Nonstandard Growth Conditions + Show 8 more

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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 equation. We prove the existence of a bounded weak solution and study its localization (vanishing) properties.

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