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Sbornik: Mathematics, 2017, Volume 208, Issue 8, Pages 1187–1206
DOI: https://doi.org/10.1070/SM8691
(Mi sm8691)
 

This article is cited in 26 scientific papers (total in 26 papers)

Uniqueness of the renormalized solution of an elliptic-parabolic problem in anisotropic Sobolev-Orlicz spaces

F. Kh. Mukminov

Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa
References:
Abstract: We consider the first mixed problem for a class of anisotropic elliptic-parabolic equations with double variable nonlinearities in a cylindrical domain $(0,T)\times\Omega$. The domain $\Omega\subset\mathbb{R}^n$ can be unbounded. The uniqueness of the renormalized solution is proved using Kruzhkov's method of doubling the variable $t$. The same result is established for an equation with non-power law nonlinearities.
Bibliography: 24 titles.
Keywords: anisotropic parabolic equation, renormalized solution, variable nonlinearity, uniqueness of solution, $N$-function.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-07920-а
This research was supported by the Russian Foundation for Basic Research (grant no. 15-01-07920-a).
Received: 04.03.2016 and 20.05.2016
Bibliographic databases:
Document Type: Article
UDC: 517.954+517.956.45+517.958:531.72
MSC: Primary 35K55; Secondary 35A01, 35B05, 35B40, 35K20
Language: English
Original paper language: Russian
Citation: F. Kh. Mukminov, “Uniqueness of the renormalized solution of an elliptic-parabolic problem in anisotropic Sobolev-Orlicz spaces”, Sb. Math., 208:8 (2017), 1187–1206
Citation in format AMSBIB
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\paper Uniqueness of the renormalized solution of an elliptic-parabolic problem in~anisotropic Sobolev-Orlicz spaces
\jour Sb. Math.
\yr 2017
\vol 208
\issue 8
\pages 1187--1206
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Linking options:
  • https://www.mathnet.ru/eng/sm8691
  • https://doi.org/10.1070/SM8691
  • https://www.mathnet.ru/eng/sm/v208/i8/p106
  • This publication is cited in the following 26 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
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    Russian version PDF:59
    English version PDF:41
    References:70
    First page:32
     
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