Geodesic
On a~well posed difference scheme for the problem of piston moving in viscous barotrope conducting gas
Matematičeskoe modelirovanie, Tome 3 (1991) no. 4, pp. 67-77.

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The difference scheme mentioned in the title is constructed. Its convergence to the differential problem is proved. 
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     title = {On a~well posed difference scheme for the problem of piston moving in viscous barotrope conducting gas},
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J. E. Berniasov; Sh. S. Smagulov. On a~well posed difference scheme for the problem of piston moving in viscous barotrope conducting gas. Matematičeskoe modelirovanie, Tome 3 (1991) no. 4, pp. 67-77. http://geodesic.mathdoc.fr/item/MM_1991_3_4_a7/