Geodesic
On the Generalization of Conservation Law Theory to Certain Degenerate Parabolic Systems of Equations Describing Processes of Compressible Two-Phase Multicomponent Filtration
Matematičeskie zametki, Tome 89 (2011) no. 2, pp. 300-315

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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.
Keywords: degenerate parabolic system of equations, two-phase multicomponent filtration, conservation laws, Riemann problem, entropy, Darcy's law
Mots-clés : Hugoniot relation. 
@article{MZM_2011_89_2_a11,
     author = {Yu. G. Rykov},
     title = {On the {Generalization} of {Conservation} {Law} {Theory} to {Certain} {Degenerate} {Parabolic} {Systems} of {Equations} {Describing} {Processes} of {Compressible} {Two-Phase} {Multicomponent} {Filtration}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {300--315},
     publisher = {mathdoc},
     volume = {89},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_2_a11/}
}
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Yu. G. Rykov. On the Generalization of Conservation Law Theory to Certain Degenerate Parabolic Systems of Equations Describing Processes of Compressible Two-Phase Multicomponent Filtration. Matematičeskie zametki, Tome 89 (2011) no. 2, pp. 300-315. http://geodesic.mathdoc.fr/item/MZM_2011_89_2_a11/