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Sibirskii Zhurnal Industrial'noi Matematiki, 2022, Volume 25, Number 4, Pages 206–220
DOI: https://doi.org/10.33048/SIBJIM.2021.25.416 (Mi sjim1206) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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

Ar. S. Tersenov

Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
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DOI: https://doi.org/10.33048/SIBJIM.2021.25.416
Abstract: 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.
Keywords: anisotropic parabolic equations, viscosity solutions, time-dependent exponents. .
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0008
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.
Received: 05.07.2022
Revised: 05.08.2022
Accepted: 29.09.2022
English version:
Journal of Applied and Industrial Mathematics, 2022, Volume 16, Issue 4, Pages 821–833
DOI: https://doi.org/10.1134/S1990478922040214
Document Type: Article
UDC: 517.95
Language: Russian
Citation: Ar. S. Tersenov, “On existence of viscosity solutions for anisotropic parabolic equations with time-dependent exponents”, Sib. Zh. Ind. Mat., 25:4 (2022), 206–220; J. Appl. Industr. Math., 16:4 (2022), 821–833
Citation in format AMSBIB
\Bibitem{Ter22}
\by Ar.~S.~Tersenov
\paper On existence of viscosity solutions for anisotropic parabolic equations with time-dependent exponents
\jour Sib. Zh. Ind. Mat.
\yr 2022
\vol 25
\issue 4
\pages 206--220
\mathnet{http://mi.mathnet.ru/sjim1206}
\transl
\jour J. Appl. Industr. Math.
\yr 2022
\vol 16
\issue 4
\pages 821--833
\crossref{https://doi.org/10.1134/S1990478922040214}
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