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We prove the so-called generalized Haff's law yielding the optimal algebraiccooling rate of the temperature of a granular gas described by the homogeneousBoltzmann equation for inelastic interactions with non constant restitutioncoefficient. Our analysis is carried through a careful study of the infinitesystem of moments of the solution to the Boltzmann equation for granular gasesand precise Lp estimates in the selfsimilar variables. In the process, wegeneralize several results on the Boltzmann collision operator obtainedrecently for homogeneous granular gases with constant restitution coefficientto a broader class of physical restitution coefficients that depend on thecollision impact velocity. This generalization leads to the so-calledL1-exponential tails theorem. for this model.

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