Dissipation ratio dependent solutions of the Riemann problem for the conservation laws system representing chemical flooding

We study the solutions of the Riemann problem arising in chemical flooding models. Vanishing viscosity admissibility criterion is used to distinguish physically meaningful weak solutions. We demonstrate that when the flow function depends non-monotonically on the chemical agent concentration, non-classical undercompressive shocks appear. We prove the monotonic dependence of the shock velocity on the ratio of dissipative coefficients. For that purpose we classify the phase portraits for the travelling wave dynamical systems and study the saddle-saddle connections.
Joint work with F.Bakharev, A.Enin, Yu.Petrova.