Shock waves and two phase porous media flows

Models for porous media flow with multiple fluids (water and oil, for example) are important for studying techniques such as geological storage of CO2 and water driven oil recovery. These models consist of conservation laws and often contain nonlinearities that preclude the existence of classical solutions. Hans van Duijn and Sorin Pop discuss important aspects of the theory of hyperbolic conservation laws, in particular existence and uniqueness of weak solutions, admissibility conditions and shock solutions. This theory explains saturation overshoots occurring in porous media flows under non-equilibrium conditions.