On existence of viscosity solutions for anisotropic parabolic equations with time-dependent exponents

Ar. S. Tersenov

Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 4, pp. 206-220.

Résumé

In the present paper we consider the Cauchy—Dirichlet problem for anisotropic parabolic equation with gradient term which does not satisfy Bernstein—Nagumo condition. The existence and uniqueness of viscosity solution for this problem is proved. This solution is Hølder continuous in time and Lipschitz continuous in spatial variables.

Détail

Mots-clés : anisotropic parabolic equations
Keywords: viscosity solutions, time-dependent exponents. .

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