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The Riemann problem for multicomponent polymer flooding. (English) Zbl 0686.35077
The paper considers the construction of global solutions of the Riemann problem for the nonstrictly hyperbolic system of conservation laws $$ s\sb t+f(s,c\sb 1,...,c\sb n)=0;\quad [sc\sb i+a\sb i(c\sb i)]\sb t+[c\sb if(s,c\sb 1,...,c\sb n)]\sb x=0,\quad i=1,2,...,n, $$ where $(s,c\sb 1,...,c\sb n)\in [0,1]\sp{n+1}$; $f(\cdot,c\sb 1,...,c\sb n)$ is increasing, with an inflection point, $f(s,c\sb 1,...,c\sb{i- 1},\cdot,c\sb{i+1},...,c\sb n)$ is decreasing for all i, $a\sb i(\cdot)$ is of Langmuir type, i.e. is concave, increasing and $a\sb i(0)=0.$ First elementary waves are determined: rarefaction waves, i.e. smooth solutions and shock waves. The general solution is obtained by composing waves and constant states.
Reviewer: V.Rasvan

MSC:
35L65Conservation laws
76S05Flows in porous media; filtration; seepage
35L67Shocks and singularities
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