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Matematicheskie Trudy, 2002, Volume 5, Number 2, Pages 38–91 (Mi mt108)  
This article is cited in 1 scientific paper (total in 1 paper)

Regularity of a Solution to the Multidimensional Free Boundary Problem for the Porous Medium Equation

B. V. Bazalii, N. V. Krasnoshchek

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences
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Abstract: The regularity properties of solutions to the initial boundary value problem with free boundary for the nonlinear degenerate equation $u_t=\Delta(u^m)$, $m>1$, are studied in the multi-dimensional case. The condition $u=0$ holds on the free boundary whose velocity obeys the Darcy law. The differential properties of the free boundary are established in dependence on the smoothness of the initial data.
Key words: porous medium equation, free boundary, regularity of solution, Green function.
Received: 17.12.2001
Bibliographic databases:
UDC: 517.946
Language: Russian
Citation: B. V. Bazalii, N. V. Krasnoshchek, “Regularity of a Solution to the Multidimensional Free Boundary Problem for the Porous Medium Equation”, Mat. Tr., 5:2 (2002), 38–91; Siberian Adv. Math., 13:3 (2003), 1–53
Citation in format AMSBIB
\Bibitem{BazKra02}
\by B.~V.~Bazalii, N.~V.~Krasnoshchek
\paper Regularity of a~Solution to the~Multidimensional Free Boundary Problem for the~Porous Medium Equation
\jour Mat. Tr.
\yr 2002
\vol 5
\issue 2
\pages 38--91
\mathnet{http://mi.mathnet.ru/mt108}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1944066}
\zmath{https://zbmath.org/?q=an:1013.76093}
\elib{https://elibrary.ru/item.asp?id=9532588}
\transl
\jour Siberian Adv. Math.
\yr 2003
\vol 13
\issue 3
\pages 1--53
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические труды Siberian Advances in Mathematics
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    References:83
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