Stability of Maxwellian states for the Broadwell model of the extended Boltzmann equation

The extended Boltzmann equation for test particles in an absorbing and generating background plane medium with generalized boundary conditions is discretized according to the classical Broadwell scheme, which allows three dimensions to the molecular velocity vector. Stability of Maxwellian states to small space dependent perturbations is studied analytically and numerically, both on the whole real line and on a finite interval. Results prove, among other things, the existence, for the boundary value problem, of regions of positive measure in the parameter space which yield instability, due to the presence of a positive eigenvalue. (Author)