Interactions in general continua with microstructure

This paper studies the behavior of the one dimensional Broadwell model of a discrete three velocity gas on a bounded domain 0 x 1 with specularly reflective boundary condition at x = 0, 1. For smooth initial data we show that the initial boundary value problem possesses a unique smooth solution which tends as t to a free state consisting of traveling waves f _1e (x – ct), f _2e (x + ct), f _3e (x) where each f _ie is 2-periodic. The convergence is in the weak* topology of an appropriate Orlicz-Banach state space. No smallness assumptions are made on the data.In memory of Ronald J. DiPerna