caa a22 4500 46789132X CHVBK 20180406152750.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s10955-006-9097-8 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9097-8 Cooling Process for Inelastic Boltzmann Equations for Hard Spheres, Part II: Self-Similar Solutions and Tail Behavior [Elektronische Daten] [S. Mischler, C. Mouhot] We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients. We prove the existence of self-similar solutions, and we give pointwise estimates on their tail. We also give general estimates on the tail and the regularity of generic solutions. In particular we prove Haff's law on the rate of decay of temperature, as well as the algebraic decay of singularities. The proofs are based on the regularity study of a rescaled problem, with the help of the regularity properties of the gain part of the Boltzmann collision integral, well-known in the elastic case, and which are extended here in the context of granular gases. Springer Science + Business Media, Inc., 2006 Boltzmann equation nationallicence inelastic hard spheres nationallicence granular gas nationallicence cooling process nationallicence Haff's law nationallicence self-similar solutions nationallicence regularity of the collision operator nationallicence tail behavior nationallicence Mischler S. Ceremade, Université Paris IX-Dauphine, place du Mal DeLattre de Tasigny, 75016, Paris, France aut Mouhot C. Ceremade, Université Paris IX-Dauphine, place du Mal DeLattre de Tasigny, 75016, Paris, France aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 703-746 0022-4715 124:2-4<703 2006 124 10955 https://doi.org/10.1007/s10955-006-9097-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9097-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Mischler S. Ceremade, Université Paris IX-Dauphine, place du Mal DeLattre de Tasigny, 75016, Paris, France aut NATIONALLICENCE 700 1- Mouhot C. Ceremade, Université Paris IX-Dauphine, place du Mal DeLattre de Tasigny, 75016, Paris, France aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 703-746 0022-4715 124:2-4<703 2006 124 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer