Broadwell Model and Conservative Supersonic Boundary

Abstract

In this paper, we consider an initial-boundary value problem for the Broadwell model with a supersonic physical boundary. Here, we pose a conservative boundary condition which preserves the total number of particles. We show that the solution converges pointwise to a boundary layer exponentially, when the perturbations of the initial data to the equilibrium state are sufficiently small, by using Green's function as established in Lan et al. (Netw Heterog Media 1:167-183, 2006), weighted energy estimates and by constructing a pair of anti-derivatives to convert the conservative boundary condition into a dissipative boundary condition with conservation laws together with an a priori chosen boundary layer. © 2010 Springer-Verlag.