# Stability, Convergence to Self-Similarity and Elastic Limit for the Boltzmann Equation for Inelastic Hard Spheres

@article{Mischler2009StabilityCT, title={Stability, Convergence to Self-Similarity and Elastic Limit for the Boltzmann Equation for Inelastic Hard Spheres}, author={St{\'e}phane Mischler and Cl{\'e}ment Mouhot}, journal={Communications in Mathematical Physics}, year={2009}, volume={288}, pages={431-502} }

We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients$${\alpha \in [0,1]}$$ . In the physical regime of a small inelasticity (that is $${\alpha \in [\alpha_*,1)}$$ for some constructive $${\alpha_* \in [0,1)}$$) we prove uniqueness of the self-similar profile for given values of the restitution coefficient $${\alpha \in [\alpha_*,1)}$$ , the mass and the momentum; therefore we deduce the…

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