In this talk we discuss discretization based dispersive-dissipative regularization of mixed type systems and derive the resulting closure conditions known as kinetic relations. Algebraic kinetic relations link velocities of the undercompressed jump discontinuities with the corresponding driving forces and are widely used to model dynamical response of phase boundaries. To capture the effects of discretization more faithfully we propose to replace algebraic kinetic relations with differential kinetic equations which involve some specially selected collective variables characterizing not only the location of the discontinuity but also the structure of the transition region. Joint work with A. Vainchtein.