Equilibrium Solution to the Inelastic Boltzmann Equation Driven by a   Particles Thermal Bath
  We show the existence of smooth stationary solutions for the inelastic Boltzmann equation under the thermalization induced by a host-medium with a fixed distribution. This is achieved by controlling the Lp-norms, the moments and the regularity of the solutions for the Cauchy problem together with arguments related to a dynamical proof for the existence of stationary states. 
Marzia Bisi, Jose A. Carrillo, Bertrand Lods