Geodesic
A~priori smoothness of solutions for number of equations of a~changing type
Matematičeskoe modelirovanie, Tome 2 (1990) no. 9, pp. 145-153.

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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. 
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     author = {M. M. Lavrent'ev (Jn.)},
     title = {A~priori smoothness of solutions for number of equations of a~changing type},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {145--153},
     publisher = {mathdoc},
     volume = {2},
     number = {9},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1990_2_9_a12/}
}
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M. M. Lavrent'ev (Jn.). A~priori smoothness of solutions for number of equations of a~changing type. Matematičeskoe modelirovanie, Tome 2 (1990) no. 9, pp. 145-153. http://geodesic.mathdoc.fr/item/MM_1990_2_9_a12/