Large time behavior of the broadwell model of a discrete velocity gas with specularly reflective boundary conditions

✍ Scribed by M. Slemrod

• Publisher: Springer
• Year: 1990
• Tongue: English
• Weight: 896 KB
• Volume: 111
• Category: Article
• ISSN: 0003-9527
• DOI: 10.1007/bf00376025

✦ Synopsis

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-+ oo to a free state consisting of traveling waves fle(X-et), f2e(X -t-Ct), f3e(X) where each f/e 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.