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

This article is cited in 5 scientific papers (total in 5 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

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  mathscinet  isi
    2. A. K. Gushchin, “The boundary values of solutions of an elliptic equation”, Sb. Math., 210:12 (2019), 1724–1752  mathnet  crossref  crossref  mathscinet  isi  elib
    3. F. Kh. Mukminov, “Existence of a Renormalized Solution to an Anisotropic Parabolic Problem for an Equation with Diffuse Measure”, Proc. Steklov Inst. Math., 306 (2019), 178–195  mathnet  crossref  crossref  isi  elib
    4. V. F. Vil'danova, “Existence and uniqueness of a weak solution of an integro-differential aggregation equation on a Riemannian manifold”, Sb. Math., 211:2 (2020), 226–257  mathnet  crossref  crossref  isi  elib
    5. A. K. Guschin, “Obobscheniya prostranstva nepreryvnykh funktsii; teoremy vlozheniya”, Matem. sb., 211:11 (2020), 54–71  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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