caa a22 4500 467891338 CHVBK 20180406152750.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s10955-006-9096-9 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9096-9 Cooling Process for Inelastic Boltzmann Equations for Hard Spheres, Part I: The Cauchy Problem [Elektronische Daten] [S. Mischler, C. Mouhot, M. Ricard] We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and the relative velocity as well as the sticky particles model. We prove (local in time) non-concentration estimates in Orlicz spaces, from which we deduce weak stability and existence theorem. Strong stability together with uniqueness and instantaneous appearance of exponential moments are proved under additional smoothness assumption on the initial datum, for a restricted class of collision rates. Concerning the long-time behaviour, we give conditions for the cooling process to occur or not in finite time. Springer Science + Business Media, Inc., 2006 Inelastic Boltzmann equation nationallicence hard spheres nationallicence variable restitution coefficient nationallicence Cauchy problem nationallicence Orlicz spaces nationallicence cooling process 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 Ricard M. Facultad de Matemática y Computación, Universidad de La Habana, 10400, C. Habana, Cuba aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 655-702 0022-4715 124:2-4<655 2006 124 10955 https://doi.org/10.1007/s10955-006-9096-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9096-9 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 700 1- Ricard M. Facultad de Matemática y Computación, Universidad de La Habana, 10400, C. Habana, Cuba aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 655-702 0022-4715 124:2-4<655 2006 124 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer