Free cooling and high-energy tails of granular gases with variable restitution coefficient

We prove the so-called generalized Haff's law yielding the optimal algebraic cooling rate of the temperature of a granular gas described by the homogeneous Boltzmann equation for inelastic interactions with non constant restitution coefficient. Our analysis is carried through a careful study of the infinite system of moments of the solution to the Boltzmann equation for granular gases and precise Lp estimates in the selfsimilar variables. In the process, we generalize several results on the Boltzmann collision operator obtained recently for homogeneous granular gases with constant restitution coefficient to a broader class of physical restitution coefficients that depend on the collision impact velocity. This generalization leads to the so-called L1-exponential tails theorem. for this model.