Parametric dependence of phase boundary solution to model kinetic equation

Abstract

In this paper we study travelling wave solutions of a four-velocity model of van der Waals fluids, connecting two equilibrium states, which are saddle critical points of the corresponding dynamic system. Solutions of this type are interpreted as dynamic phase transitions. We look for solutions which are a perturbation of the Maxwell line solution describing equilibrium phase changes. Using the Implicit Function Theorem we show that, under some additional assumptions, there exists a unique travelling wave to our model, and that it is continuously differentiable with respect to the parameters of the problem. Also, given the left state of rest, we obtain an approximate expression for the wave speed. From this formula we infer that the "kinetic" wave speed is different from the one obtained from the hydrodynamic approximation.