Stability of a resonant system of conservation laws modeling polymer flow with gravitation.

*(English)*Zbl 0977.35083The 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.

Reviewer: Evgeniy Panov (Novgorod)

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\textit{C. Klingenberg} and \textit{N. H. Risebro}, J. Differ. Equations 170, No. 2, 344--380 (2001; Zbl 0977.35083)

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