Chapter

Free Boundary Problems

Volume 154 of the series International Series of Numerical Mathematics pp 33-44

Parabolic Equations with Anisotropic Nonstandard Growth Conditions

  • S. AntontsevAffiliated withDepartamento de Matemática, Universidade da Beira Interior
  • , S. ShmarevAffiliated withDepartamento de Matemática, Universidade da Beira InteriorDepartaménto de Matematicas, Universidad de Oviedo

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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.

Keywords

Nonlinear parabolic equation nonstandard growth conditions anisotropic nonlinearity localization of solutions