Geodesic
Functional-valued solutions to conservation laws and difference schemes
Matematičeskoe modelirovanie, Tome 3 (1991) no. 7, pp. 78-100.

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A new class of generalized solutions to system of conservation laws proposed lately – functional-valued and solutions in the mean – is considered. Some existence and convergence theorems are proved. Definition of $\mathscr{A}$-system, whose Lax's difference solutions converge to functional-valued solutions for polydimensional Cauchy problem, is proposed. Convergence of Lax's difference solution for isentropic gas dynamics to a functional-valued one is based. A new family of floating net implicit difference schemes for isentropic gas dynamics is proposed and convergence of its solutions to functional-valued one for original problem is proved. 
@article{MM_1991_3_7_a8,
     author = {N. C. Sklobovsky and V. A. Tupchiev},
     title = {Functional-valued solutions to conservation laws and difference schemes},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {78--100},
     publisher = {mathdoc},
     volume = {3},
     number = {7},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1991_3_7_a8/}
}
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N. C. Sklobovsky; V. A. Tupchiev. Functional-valued solutions to conservation laws and difference schemes. Matematičeskoe modelirovanie, Tome 3 (1991) no. 7, pp. 78-100. http://geodesic.mathdoc.fr/item/MM_1991_3_7_a8/