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Sbornik: Mathematics, 2018, Volume 209, Issue 5, Pages 714–738
DOI: https://doi.org/10.1070/SM8921 (Mi sm8921) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Existence of a renormalized solution to an anisotropic parabolic problem with variable nonlinearity exponents

F. Kh. Mukminovab

a Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa
b Ufa State Aviation Technical University
English version PDF (577 kB) Citations (8)
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DOI: https://doi.org/10.1070/SM8921
Abstract: The first boundary value problem is considered for a certain class of anisotropic parabolic equations with variable nonlinearity exponents in a cylindrical domain $( 0,T)\times\Omega$, where $\Omega$ is a bounded domain. The parabolic term in the equation has the form $(\beta(x,u))_t$ and is determined by the function $\beta(x,r)\in L_1(\Omega)$, where $r\in \mathbb R$, which only satisfies the Carathéodory condition and is increasing in $r$. The existence of a weak and a renormalized solution is proved.
Bibliography: 26 titles.
Keywords: anisotropic parabolic equation, renormalized solution, variable nonlinearity exponents, existence of a solution.
Received: 02.02.2017 and 25.10.2017
Russian version:
Matematicheskii Sbornik, 2018, Volume 209, Number 5, Pages 120–144
DOI: https://doi.org/10.4213/sm8921
Bibliographic databases:
Document Type: Article
UDC: 517.954+517.956.45+517.958:531.72
MSC: 35K59
Language: English
Original paper language: Russian
Citation: F. Kh. Mukminov, “Existence of a renormalized solution to an anisotropic parabolic problem with variable nonlinearity exponents”, Mat. Sb., 209:5 (2018), 120–144; Sb. Math., 209:5 (2018), 714–738
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:66
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