Mathematical and numerical study of a system of conservation laws (Q2644648)

The system consisting of the equations \((f(u))_t-(a(u)v+b(u))_x=0\) and \(u_t-(c(u)v+d(u))_x=0\) for two functions \(u,v\) depending on \(x\) and \(t\) arises in the modelling of miscible fluids in a porous medium. The authors prove the existence of a weak entropy solution and the existence of self-similar solutions by means of a convergence result for a certain finite volume scheme.