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Matematicheskoe modelirovanie, 1990, Volume 2, Number 9, Pages 145–153
(Mi mm2458)
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This article is cited in 1 scientific paper (total in 1 paper)
Computational methods and algorithms
A priori smoothness of solutions for number of equations of a changing type
M. M. Lavrent'ev (Jn.) Institute of Mathematics, Siberian Branch of USSR Academy of Sciences
Abstract:
For number of non-linear equations of the type
$$
U_t=a''(U_x)U_{xx}+2\mu U U_x,
$$
with sign changing function $a''(\xi)$ ($a''(\xi)\geqslant\delta>0$, $|\xi|\geqslant N$) a priori estimation $\|u_x\|_{W_2^{1,1}}$ for smooth solutions in obtained. Different form the previous investigations the case of $\mu\ne0$ and the more general form of the function $a$ are considered,Connection is marked of the problem considered with so-called Cahn–Hilliard equation by which the phase separation in the melts can be simulated.
Received: 20.05.1990
Citation:
M. M. Lavrent'ev (Jn.), “A priori smoothness of solutions for number of equations of a changing type”, Matem. Mod., 2:9 (1990), 145–153
Linking options:
https://www.mathnet.ru/eng/mm2458 https://www.mathnet.ru/eng/mm/v2/i9/p145
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Abstract page: | 234 | Full-text PDF : | 107 | References: | 1 | First page: | 1 |
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