Two proofs of Haff’s law for dissipative gases: The use of entropy and the weakly inelastic regime

We revisit our recent contribution (Alonso and Lods 2010) [1] and give two simpler proofs of the so-called Haff’s law for granular gases (with non-necessarily constant restitution coefficient). The first proof is based upon the use of entropy and asserts that Haff’s law holds whenever the initial datum is of finite entropy. The second proof uses only the moments of the solution and holds in a weakly inelastic regime clearly defined whenever the restitution coefficient is non-constant.