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This article is cited in 1 scientific paper (total in 1 paper)
On the structure of weak solutions of the Riemann problem for a degenerate nonlinear diffusion equation
E. Yu. Panovab a Research and Development Center, Novgorod the Great, Russia
b Yaroslav-the-Wise Novgorod State University, Novgorod the Great, Russia
Abstract:
An explicit form of weak solutions to the Riemann problem for a degenerate nonlinear parabolic equation with a piecewise constant diffusion coefficient is found. It is shown that the lines of phase transitions (free boundaries) correspond to the minimum point of some strictly convex and coercive function of a finite number of variables. A similar result is true for Stefan's problem. In the limit, when the number of phases tends to infinity, there arises a variational formulation of self-similar solutions to the equation with an arbitrary nonnegative diffusion function.
Keywords:
degenerate nonlinear parabolic equation, Riemann problem, Stefan problem, weak solution, phase transition, self-similar solution.
Citation:
E. Yu. Panov, “On the structure of weak solutions of the Riemann problem for a degenerate nonlinear diffusion equation”, CMFD, 69, no. 4, PFUR, M., 2023, 676–684
Linking options:
https://www.mathnet.ru/eng/cmfd521 https://www.mathnet.ru/eng/cmfd/v69/i4/p676
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Abstract page: | 57 | Full-text PDF : | 31 | References: | 17 |
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