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 Dal'nevost. Mat. Zh., 2013, Volume 13, Number 2, Pages 250–272 (Mi dvmg266)

Solvability quasi-linear parabolic equation in domains with picewise monotone boundary

A. G. Podgaev, K. V. Lisenkov

Pacific National University, Khabarovsk

Abstract: We investigate the existence of regular solutions for the quasilinear parabolic equation in non-cylindrical domain with boundary of class $W^1_2$. The equation can degenerate to the decision. Approximate solutions are constructed using the projection method of the family of projectors depending on the time parameter. We prove that a limit of these solutions will be the solution of the problem. To justify the existence of the limit methods are used for the functions of the compact scale of Banach spaces.

Key words: existence, a quasi-linear parabolic equation, non-cylindrical domains, the projection method, the compactness, the scale of Banach spaces

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Document Type: Article
UDC: 517.95 + 519.633
MSC: Primary 35K59; Secondary 65N30

Citation: A. G. Podgaev, K. V. Lisenkov, “Solvability quasi-linear parabolic equation in domains with picewise monotone boundary”, Dal'nevost. Mat. Zh., 13:2 (2013), 250–272

Citation in format AMSBIB
\Bibitem{PodLis13} \by A.~G.~Podgaev, K.~V.~Lisenkov \paper Solvability quasi-linear parabolic equation in domains with picewise monotone boundary \jour Dal'nevost. Mat. Zh. \yr 2013 \vol 13 \issue 2 \pages 250--272 \mathnet{http://mi.mathnet.ru/dvmg266}