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 Tr. Mat. Inst. Steklova, 2019, Volume 306, Pages 192–209 (Mi tm4002)

Existence of a Renormalized Solution to an Anisotropic Parabolic Problem for an Equation with Diffuse Measure

F. Kh. Mukminov

Institute of Mathematics with Computing Centre, Ufa Federal Research Centre of the Russian Academy of Sciences, ul. Chernyshevskogo 112, Ufa, 450008 Russia

Abstract: The first initial–boundary value problem is considered for a class of anisotropic parabolic equations with variable nonlinearity exponents and a diffuse measure on the right-hand side in a cylindrical domain $(0,T)\times \Omega$. The domain $\Omega$ is bounded. The existence of a renormalized solution is proved.

 Funding Agency Grant Number Russian Foundation for Basic Research 18-01-00428 This work was supported by the Russian Foundation for Basic Research, project no. 18-01-00428.

DOI: https://doi.org/10.4213/tm4002

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English version:
Proceedings of the Steklov Institute of Mathematics, 2019, 306, 178–195

Bibliographic databases:

UDC: 517.954+517.956.45+517.958:531.72
Revised: October 11, 2018
Accepted: June 11, 2019

Citation: F. Kh. Mukminov, “Existence of a Renormalized Solution to an Anisotropic Parabolic Problem for an Equation with Diffuse Measure”, Mathematical physics and applications, Collected papers. In commemoration of the 95th anniversary of Academician Vasilii Sergeevich Vladimirov, Tr. Mat. Inst. Steklova, 306, Steklov Math. Inst. RAS, Moscow, 2019, 192–209; Proc. Steklov Inst. Math., 306 (2019), 178–195

Citation in format AMSBIB
\Bibitem{Muk19} \by F.~Kh.~Mukminov \paper Existence of a Renormalized Solution to an Anisotropic Parabolic Problem for an Equation with Diffuse Measure \inbook Mathematical physics and applications \bookinfo Collected papers. In commemoration of the 95th anniversary of Academician Vasilii Sergeevich Vladimirov \serial Tr. Mat. Inst. Steklova \yr 2019 \vol 306 \pages 192--209 \publ Steklov Math. Inst. RAS \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm4002} \crossref{https://doi.org/10.4213/tm4002} \elib{https://elibrary.ru/item.asp?id=43228719} \transl \jour Proc. Steklov Inst. Math. \yr 2019 \vol 306 \pages 178--195 \crossref{https://doi.org/10.1134/S008154381905016X} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000511670100016} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85077363513} 

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2. L. M. Kozhevnikova, “Renormalizovannye resheniya ellipticheskikh uravnenii s peremennymi pokazatelyami i dannymi v vide obschei mery”, Matem. sb., 211:12 (2020), 83–122
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