Large-time behavior of the Broadwell model of a discrete velocity gas (Q581147)

We study the behavior of solutions of the one-dimensional Broadwell model of a discrete velocity gas [\textit{J. E. Broadwell}, Phys. Fluids 7, 1243- 1247 (1964; Zbl 0123.211)]. The particles have velocity \(\pm 1\) or 0; the total mass is assumed finite. We show that at large time the interaction is negligible and the solution tends to a free state in which all the mass travels outward at speed 1. The limiting behavior is stable with respect to the initial state. No smallness assumptions are made.