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Mat. Sb., 2018, Volume 209, Number 5, Pages 120–144 (Mi msb8921)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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.

DOI: https://doi.org/10.4213/sm8921

Full text: PDF file (717 kB)
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English version:
Sbornik: Mathematics, 2018, 209:5, 714–738

Bibliographic databases:

UDC: 517.954+517.956.45+517.958:531.72
MSC: 35K59
Received: 02.02.2017 and 25.10.2017

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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  • https://doi.org/10.4213/sm8921
  • http://mi.mathnet.ru/eng/msb/v209/i5/p120

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kozhevnikova L.M., “On Solutions of Anisotropic Elliptic Equations With Variable Exponent and Measure Data”, Complex Var. Elliptic Equ.  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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