Dual-family viscous shock waves in \(n\) conservation laws with application to multi-phase flow in porous media (Q2505510)

The authors study shock waves in general systems of conservation laws. The requirement that the shocks possess the viscous profiles produces new type of shocks, the so called dual-family shocks \(S_{i,j}\), associated with the \(i\)-th characteristic family on the left and the \(j\)-th characteristic family on the right (the case \(i=j\) corresponds to the classical Lax's shocks). The authors introduce defining equations relating states and speeds of shock waves \(S_{i,y}\) and give their stability analysis. Possible structures of solutions to the Riemann problem containing \(S_{i,j}\) shocks are completely described. The obtained results are applied to the models for multi-phase flow in porous media. In particular, all possible types of \(S_{i,j}\) shocks with \(i>j\) are detected and studied.