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On the Existence of Viscosity Solutions of Anisotropic Parabolic Equations with Time-Dependent Anisotropy Exponents

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Abstract

We consider the Cauchy–Dirichlet problem for an anisotropic parabolic equation with a gradient term that does not satisfy the Bernstein–Nagumo condition. The existence and uniqueness of a viscosity solution of this problem is proved. This solution is Hölder continuous in time and Lipschitz continuous in the spatial variables.

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Funding

This work was carried out within the framework of the state order for the Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, project no. FWNF-2022-0008.

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  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    Ar. S. Tersenov

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  1. Ar. S. Tersenov
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Correspondence to Ar. S. Tersenov.

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Translated by V. Potapchouck

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Tersenov, A.S. On the Existence of Viscosity Solutions of Anisotropic Parabolic Equations with Time-Dependent Anisotropy Exponents. J. Appl. Ind. Math. 16, 821–833 (2022). https://doi.org/10.1134/S1990478922040214

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  • DOI: https://doi.org/10.1134/S1990478922040214

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