Stability of the Riemann semigroup with respect to the kinetic condition

A phase transition is a jump discontinuity in a solution u to (1.1) between states u(t, x−) and u(t, x+) belonging to different phases. Physical models leading to this setting are provided by liquid vapor phase transitions, elastodynamics or combustion models, see [2, 7, 8, 9, 19, 20] and the references therein. Typically, in the case (1.2) the Riemann problem for (1.1) turns out to be underdetermined and further conditions need to be supplemented. Physically, various criteria have been devised: viscosity [20], viscocapillarity [19] or other kinetic conditions [2]. From an analytical point of view, the above criteria can be described through the generalized kinetic condition

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