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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 7, Pages 1214–1229 (Mi zvmmf4562)  
This article is cited in 30 scientific papers (total in 30 papers)

On the behavior of solutions to the Cauchy problem for a degenerate parabolic equation with inhomogeneous density and a source

A. V. Martynenko, A. F. Tedeev

Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, ul. R. Lyuksemburg 74, Donetsk, 340114, Ukraine
Full-text PDF (1344 kB) Citations (30)
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Abstract: The Cauchy problem for a degenerate parabolic equation with a source and inhomogeneous density of the form
$$ \rho(x)\frac{\partial u}{\partial t}=\operatorname{div}(u^{m-1}|Du|^{\lambda-1}Du)+\rho(x)u^p. $$
is studied. Time global existence and nonexistence conditions are found for a solution to the Cauchy problem. Exact estimates of the solution are obtained in the case of global solvability.
Key words: equations with inhomogeneous density, degenerate parabolic equation, blowup solution, existence and nonexistence theorems.
Received: 15.01.2007
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 7, Pages 1145–1160
DOI: https://doi.org/10.1134/S0965542508070087
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: A. V. Martynenko, A. F. Tedeev, “On the behavior of solutions to the Cauchy problem for a degenerate parabolic equation with inhomogeneous density and a source”, Zh. Vychisl. Mat. Mat. Fiz., 48:7 (2008), 1214–1229; Comput. Math. Math. Phys., 48:7 (2008), 1145–1160
Citation in format AMSBIB
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    • This publication is cited in the following 30 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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