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Sbornik: Mathematics, 2012, Volume 203, Issue 4, Pages 581–611
DOI: https://doi.org/10.1070/SM2012v203n04ABEH004236 (Mi sm7744) 		 
This article is cited in 4 scientific papers (total in 4 papers)

The Cauchy problem for a quasilinear parabolic equation with gradient absorption

V. A. Markasheva, An. F. Tedeev

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences
English version PDF (611 kB) Citations (4) Russian version article
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DOI: https://doi.org/10.1070/SM2012v203n04ABEH004236
Abstract: The qualitative properties of solutions to the Cauchy problem for a degenerate parabolic equation containing a nonlinear operator of Baouendi-Grushin type and with gradient absorption whose density depends on time, as well as the space variables, are investigated. Bounds for the diameter of the support of the solution which are sharp with respect to time are obtained, together with its maximum. A condition which determines whether or not the phenomenon of decay to zero of the total mass of the solution occurs is discovered.
Bibliography: 35 titles.
Keywords: operator of Baouendi-Grushin type, quasilinear parabolic equation, gradient absorption, decay of the total mass of a solution, estimate for the support of the solution.
Received: 26.05.2010 and 26.08.2011
Bibliographic databases:
Document Type: Article
UDC: 517.946
MSC: Primary 35K59; Secondary 35R03
Language: English
Original paper language: Russian
Citation: V. A. Markasheva, An. F. Tedeev, “The Cauchy problem for a quasilinear parabolic equation with gradient absorption”, Sb. Math., 203:4 (2012), 581–611
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v203/i4/p131
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник Sbornik: Mathematics
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    Abstract page:899
    Russian version PDF:245
    English version PDF:36
    References:85
    First page:56
     
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