The Green's functions for the Broadwell Model in a half space problem

We study an initial boundary value problem for the Broadwell model with a supersonic physical boundary. The Green's function for an initial value problem is constructed and its detailed pointwise structure is obtained through the novel decompositions introduced in [8]. With the Green's function for initial value problem and energy estimates together, a new approach to convert a priori $L^2$-boundary data into $L^\infty$ boundary data is established for the Broadwell model. The Green's function for an initial boundary value problem is obtained. Finally, a nonlinearly time-asymptotic stability of an equilibrium state is proved.