  Consider the initial-boundary value problem for the 2-speed Carleman model of
the Boltzmann equation of the kinetic theory of gases set in some bounded
interval with boundary conditions prescribing the density of particles entering
the interval. Under the usual parabolic scaling, a nonlinear diffusion limit is
established for this problem. In fact, the techniques presented here allow
treating generalizations of the Carleman system where the collision frequency
is proportional to some power of the macroscopic density, with exponent in
[-1,1].
