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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 270, Pages 21–32 (Mi tm3011)  
This article is cited in 31 scientific papers (total in 31 papers)

Existence theorems for solutions of parabolic equations with variable order of nonlinearity

Yu. A. Alkhutov, V. V. Zhikov

Vladimir State University for the Humanities, Vladimir, Russia
Full-text PDF (210 kB) Citations (31)
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Abstract: We study the solvability of an initial-boundary value problem for second-order parabolic equations with variable order of nonlinearity. In the model case, the equation contains the $p$-Laplacian with a variable exponent $p(x,t)$. We prove that if the measurable exponent $p$ is separated from unity and infinity, then the problem has $W$- and $H$-solutions.
Received in October 2009
English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 270, Pages 15–26
DOI: https://doi.org/10.1134/S0081543810030028
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: Yu. A. Alkhutov, V. V. Zhikov, “Existence theorems for solutions of parabolic equations with variable order of nonlinearity”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 270, MAIK Nauka/Interperiodica, Moscow, 2010, 21–32; Proc. Steklov Inst. Math., 270 (2010), 15–26
Citation in format AMSBIB
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\paper Existence theorems for solutions of parabolic equations with variable order of nonlinearity
\inbook Differential equations and dynamical systems
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\publ MAIK Nauka/Interperiodica
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    • This publication is cited in the following 31 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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