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On Quasilinear Anisotropic Parabolic Equations with Time-Dependent Exponents

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Abstract

The Cauchy-Dirichlet problem for the anisotropic parabolic equation with variable exponents in the presence of a nonlinear source and gradient term is considered. We prove the existence and uniqueness of a weak solution that is Lipschitz continuous in the space variables.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Crete, Heraklion, Crete, Greece

    Al. S. Tersenov

  2. Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia

    Ar. S. Tersenov

Authors
  1. Al. S. Tersenov
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  2. Ar. S. Tersenov
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Corresponding author

Correspondence to Al. S. Tersenov.

Additional information

Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 1, pp. 201–223.

The second author was partially supported by the Russian Foundation for Basic Research (Grant 18-01-00649).

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Tersenov, A.S., Tersenov, A.S. On Quasilinear Anisotropic Parabolic Equations with Time-Dependent Exponents. Sib Math J 61, 159–177 (2020). https://doi.org/10.1134/S0037446620010140

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  • DOI: https://doi.org/10.1134/S0037446620010140

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