From microscopic to macroscopic models: Asymptotic analysis of the broadwell model toward the wave equation

This paper deals with the asymptotic analysis of the Broadwell model towards the wave equation. Appropriately scaled solutions of the Broadwell model are shown to have fluctuations that locally in time converge weakly to a limit governed by a solution of wave equations provided that the initial fluctuations are smooth. The weak limit becomes strong when the initial fluctuations converge to appropriate initial data.