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Stability of a resonant system of conservation laws modeling polymer flow with gravitation. (English) Zbl 0977.35083
The authors prove existence, uniqueness, and \(L^1\)-stability of entropy solutions to the Cauchy problem for the following resonant \(2\times 2\) system of conservation laws \[ s_t+f(s,c)_x=0, \quad (sc)_t+(cf(s,c))_x=0. \] Such system arises as a model for two phase polymer flow in porous media. The methods are based on front tracking approximations for the auxiliary scalar equation and the Kruzhkov’s entropy condition for scalar conservation laws.

35L65 Hyperbolic conservation laws
76S05 Flows in porous media; filtration; seepage
Full Text: DOI
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