# 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…

## 7 Citations

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A Fokker-Planck type equation of fractional diffusion with conservative drift has a property of regularization in fractional Sobolev spaces, as well as a gain of integrability and positivity which it uses to obtain polynomial or exponential convergence to equilibrium in weighted Lebesgue spaces.

### Inelastic Boltzmann equation driven by a particle thermal bath

- MathematicsKinetic & Related Models
- 2021

<p style='text-indent:20px;'>We consider the spatially inhomogeneous Boltzmann equation for inelastic hard-spheres, with constant restitution coefficient <inline-formula><tex-math…

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