caa a22 4500 467891532 CHVBK 20180406152750.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s10955-006-9035-9 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9035-9 Decay Rates in Probability Metrics Towards Homogeneous Cooling States for the Inelastic Maxwell Model [Elektronische Daten] [M. Bisi, J. Carrillo, G. Toscani] We quantify the long-time behavior of solutions to the nonlinear Boltzmann equation for spatially uniform freely cooling inelastic Maxwell molecules by means of the contraction property of a suitable metric in the set of probability measures. Existence, uniqueness, and precise estimates of overpopulated high energy tails of the self-similar profile proved in ref. 9 are revisited and derived from this new Liapunov functional. For general initial conditions the solutions of the Boltzmann equation are then proved to converge with computable rate as t → ∞ to the self-similar solution in this distance, which metrizes the weak convergence of measures. Moreover, we can relate this Fourier distance to the Euclidean Wasserstein distance or Tanaka functional proving also its exponential convergence towards the homogeneous cooling states. The findings are relevant in the understanding of the conjecture formulated by Ernst and Brito in refs. 15, 16, and complement and improve recent studies on the same problem of Bobylev and Cercignani(9) and Bobylev, Cercignani and one of the authors.(11) Springer Science + Business Media, Inc., 2006 inelastic collisions nationallicence Maxwell models nationallicence asymptotic behavior nationallicence Fourier metrics nationallicence Ernst-Brito conjecture nationallicence Bisi M. Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze 53/A, I-43100, Parma, Italy aut Carrillo J. ICREA-Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193, Bellaterra, Spain aut Toscani G. Dipartimento di Matematica, Università di Pavia, via Ferrata 1, I-27100, Pavia, Italy aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 625-653 0022-4715 124:2-4<625 2006 124 10955 https://doi.org/10.1007/s10955-006-9035-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9035-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bisi M. Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze 53/A, I-43100, Parma, Italy aut NATIONALLICENCE 700 1- Carrillo J. ICREA-Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193, Bellaterra, Spain aut NATIONALLICENCE 700 1- Toscani G. Dipartimento di Matematica, Università di Pavia, via Ferrata 1, I-27100, Pavia, Italy aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 625-653 0022-4715 124:2-4<625 2006 124 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer