  This is a continuation of the previous work (Takata & Noguchi, J. Stat.
Phys., 2018) that introduces the presumably simplest model of kinetic theory
for phase transition. Here, 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 the linear stability analysis that the linear neutral
curve is invariant with respect to the Knudsen number, though 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.
