TREND TO EQUILIBRIUM OF WEAK SOLUTIONS OF THE BOLTZMANN-EQUATION IN ASLAB WITH DIFFUSIVE BOUNDARY-CONDITIONS

Recently R. Illner and the author proved that, under a physically real istic truncation on the collision kernel, the Boltzmann equation in th e one-dimensional slab [0, 1] with general diffusive boundary conditio ns at 0 and 1 has a global weak solution in the traditional sense. Her e it is proved that when the Maxwellians associated with the boundary conditions at x = 0 and x = 1 are the same Maxwellian M(w), then the s olution is uniformly bounded and tends to M(w) for t --> infinity.