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On the generalization of conservation law theory to certain degenerate parabolic systems of equations describing processes of compressible two-phase multicomponent filtration

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Abstract

A degenerate parabolic system of equations of two-phase multicomponent filtration is considered. It is shown that this system can be treated as a system of conservation laws and the notions developed in the corresponding theory, such as hyperbolicity, shock waves, Hugoniot relations, stability conditions, Riemann problem, entropy, etc., can be applied to this system. The specific character of the use of such notions in the case of multicomponent filtration is demonstrated. An example of two-component mixture is used to describe the specific properties of solutions of the Riemann problem.

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  1. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    Yu. G. Rykov

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  1. Yu. G. Rykov
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Correspondence to Yu. G. Rykov.

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Original Russian Text © Yu. G. Rykov, 2011, published in Matematicheskie Zametki, 2011, Vol. 89, No. 2, pp. 300–315.

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Rykov, Y.G. On the generalization of conservation law theory to certain degenerate parabolic systems of equations describing processes of compressible two-phase multicomponent filtration. Math Notes 89, 291–303 (2011). https://doi.org/10.1134/S0001434611010342

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