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Sbornik: Mathematics, 2014, Volume 205, Issue 3, Pages 307–318
DOI: https://doi.org/10.1070/SM2014v205n03ABEH004377
(Mi sm8178)
 

This article is cited in 27 scientific papers (total in 27 papers)

Existence and uniqueness theorems for solutions of parabolic equations with a variable nonlinearity exponent

Yu. A. Alkhutov, V. V. Zhikov

Vladimir State University
References:
Abstract: The paper is concerned with the solvability of the initial-boundary value problem for second-order parabolic equations with variable nonlinearity exponents. In the model case, this equation contains the $p$-Laplacian with a variable exponent $p(x,t)$. The problem is shown to be uniquely solvable, provided the exponent $p$ is bounded away from both $1$ and $\infty$ and is log-Hölder continuous, and its solution satisfies the energy equality.
Bibliography: 18 titles.
Keywords: parabolic equation, variable nonlinearity exponent, log-Hölder continuity.
Funding agency Grant number
Russian Foundation for Basic Research 12-01-00058-а
14-01-00192-а
Ministry of Education and Science of the Russian Federation НШ-3685.2014.1
2014/13/3037
Received: 20.09.2012 and 15.01.2014
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 3, Pages 3–14
DOI: https://doi.org/10.4213/sm8178
Bibliographic databases:
Document Type: Article
UDC: 517.956.4
MSC: Primary 35K92; Secondary 46E35
Language: English
Original paper language: Russian
Citation: Yu. A. Alkhutov, V. V. Zhikov, “Existence and uniqueness theorems for solutions of parabolic equations with a variable nonlinearity exponent”, Mat. Sb., 205:3 (2014), 3–14; Sb. Math., 205:3 (2014), 307–318
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/sm8178
  • https://doi.org/10.1070/SM2014v205n03ABEH004377
  • https://www.mathnet.ru/eng/sm/v205/i3/p3
  • This publication is cited in the following 27 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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    Abstract page:1131
    Russian version PDF:301
    English version PDF:24
    References:104
    First page:106
     
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