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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. (English. Russian original) Zbl 1254.35148

Math. Notes 89, No. 2, 291-303 (2011); translation from Mat. Zametki 89, No. 2, 300-315 (2011).
Summary: 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, the 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.

MSC:

35L65 Hyperbolic conservation laws
35Q35 PDEs in connection with fluid mechanics
35L80 Degenerate hyperbolic equations
35K65 Degenerate parabolic equations
Full Text: DOI

References:

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