Exponential trend to equilibrium for the inelastic Boltzmann equation driven by a particle bath

@article{Caizo2015ExponentialTT,
  title={Exponential trend to equilibrium for the inelastic Boltzmann equation driven by a particle bath},
  author={Jos{\'e} A. Ca{\~n}izo and Bertrand Lods},
  journal={Nonlinearity},
  year={2015},
  volume={29},
  pages={1687 - 1715}
}
We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres (with constant restitution coefficient α∈(0,1)) under the thermalization induced by a host medium with a fixed Maxwellian distribution. We prove that the solution to the associated initial-value problem converges exponentially fast towards the unique equilibrium solution. The proof combines a careful spectral analysis of the linearised semigroup as well as entropy estimates. The trend towards equilibrium holds… 

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