Kinetic theory for a simple modeling of a phase transition: Dynamics out of local equilibrium

This is a continuation of previous work [J. Stat. Phys., 172, 880 (2018)] that introduces the presumably simplest model of kinetic theory for phase transition. Here the main concern is to clarify the stability of uniform equilibrium states in the kinetic regime rather than that in the continuum limit. It is found by linear stability analysis that the linear neutral curve is invariant with respect to the Knudsen number, although the transition process is dependent on the Knudsen number. In addition, numerical computations of the (nonlinear) kinetic model are performed to investigate the transition processes in detail. Numerical results show that (unexpected) incomplete transitions may happen as well as clear phase transitions.