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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
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
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
Linking options:
https://www.mathnet.ru/eng/mt108 https://www.mathnet.ru/eng/mt/v5/i2/p38
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Abstract page: | 750 | Full-text PDF : | 170 | References: | 81 | First page: | 1 |
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