On the Boltzmann Equation for Diffusively Excited Granular Media

@article{Gamba2004OnTB,
  title={On the Boltzmann Equation for Diffusively Excited Granular Media},
  author={Irene M. Gamba and Vladislav A. Panferov and C{\'e}dric Villani},
  journal={Communications in Mathematical Physics},
  year={2004},
  volume={246},
  pages={503-541}
}
We study the Boltzmann equation for a space-homogeneous gas of inelastic hard spheres, with a diffusive term representing a random background forcing. Under the assumption that the initial datum is a nonnegative L2(N) function, with bounded mass and kinetic energy (second moment), we prove the existence of a solution to this model, which instantaneously becomes smooth and rapidly decaying. Under a weak additional assumption of bounded third moment, the solution is shown to be unique. We also… 

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