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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Volume 260, Pages 180–192 (Mi tm593)  
This article is cited in 3 scientific papers (total in 3 papers)

On the Asymptotic Behavior of Solutions of Nonlinear Second-Order Parabolic Equations

V. A. Kondrat'ev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (202 kB) Citations (3)
References:
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Abstract: We study the asymptotic behavior as $t\to+\infty$ of solutions to a semilinear second-order parabolic equation in a cylindrical domain bounded in the spatial variable. We find the leading term of the asymptotic expansion of a solution as $t\to+\infty$ and show that each solution of the problem under consideration is asymptotically equivalent to a solution of some nonlinear ordinary differential equation.
Received in June 2007
English version:
Proceedings of the Steklov Institute of Mathematics, 2008, Volume 260, Pages 172–184
DOI: https://doi.org/10.1134/S0081543808010124
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: V. A. Kondrat'ev, “On the Asymptotic Behavior of Solutions of Nonlinear Second-Order Parabolic Equations”, Function theory and nonlinear partial differential equations, Collected papers. Dedicated to Stanislav Ivanovich Pohozaev on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 260, MAIK Nauka/Interperiodica, Moscow, 2008, 180–192; Proc. Steklov Inst. Math., 260 (2008), 172–184
Citation in format AMSBIB
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\paper On the Asymptotic Behavior of Solutions of Nonlinear Second-Order Parabolic Equations
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\vol 260
\pages 180--192
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • https://www.mathnet.ru/eng/tm593
  • https://www.mathnet.ru/eng/tm/v260/p180
    • This publication is cited in the following 3 articles:
    1. A. A. Kon'kov, “Maximum principle for nonlinear parabolic equations”, J. Math. Sci. (N. Y.), 234:4 (2018), 423–439  mathnet  crossref
    2. A. A. Konkov, “O printsipe maksimuma dlya odnogo klassa nelineinykh parabolicheskikh uravnenii”, Vestn. SamGU. Estestvennonauchn. ser., 2015, no. 6(128), 89–92  mathnet  elib
    3. I. V. Astashova, L. A. Bagirov, A. V. Filinovskii, G. V. Grishina, V. A. Il'in, A. A. Kon'kov, V. V. Kozlov, V. A. Nikishkin, E. V. Radkevich, N. Kh. Rozov, V. A. Sadovnichii, I. N. Sergeev, A. S. Shamaev, “Vladimir Aleksandrovich Kondrat'ev”, Diff Equat, 46:12 (2010), 1807  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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    Abstract page:486
    Full-text PDF :120
    References:108
    First page:22
     
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