The Riemann problem for multicomponent polymer flooding. (English) Zbl 0686.35077

Johansen, Thormod; Winther, Ragnar

SIAM J. Math. Anal. 20, No. 4, 908-929 (1989).

The paper considers the construction of global solutions of the Riemann problem for the nonstrictly hyperbolic system of conservation laws \[ s_ t+f(s,c_ 1,...,c_ n)=0;\quad [sc_ i+a_ i(c_ i)]_ t+[c_ if(s,c_ 1,...,c_ n)]_ x=0,\quad i=1,2,...,n, \] where \((s,c_ 1,...,c_ n)\in [0,1]^{n+1}\); \(f(\cdot,c_ 1,...,c_ n)\) is increasing, with an inflection point, \(f(s,c_ 1,...,c_{i- 1},\cdot,c_{i+1},...,c_ n)\) is decreasing for all i, \(a_ i(\cdot)\) is of Langmuir type, i.e. is concave, increasing and \(a_ i(0)=0.\)
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:

35L65	Hyperbolic conservation laws
76S05	Flows in porous media; filtration; seepage
35L67	Shocks and singularities for hyperbolic equations

Keywords:

nonstrictly hyperbolic system; rarefaction waves; general solution