caa a22 4500 445391944 CHVBK 20180317143049.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10955-011-0136-8 doi (NATIONALLICENCE)springer-10.1007/s10955-011-0136-8 Kinetic Models with Randomly Perturbed Binary Collisions [Elektronische Daten] [Federico Bassetti, Lucia Ladelli, Giuseppe Toscani] We introduce a class of Kac-like kinetic equations on the real line, with general random collisional rules which, in some special cases, identify models for granular gases with a background heat bath (Carrillo et al. in Discrete Contin. Dyn. Syst. 24(1):59-81, 2009), and models for wealth redistribution in an agent-based market (Bisi etal. in Commun. Math. Sci. 7:901-916, 2009). Conditions on these collisional rules which guarantee both the existence and uniqueness of equilibrium profiles and their main properties are found. The characterization of these stationary states is of independent interest, since we show that they are stationary solutions of different evolution problems, both in the kinetic theory of rarefied gases (Cercignani etal. in J. Stat. Phys. 105:337-352, 2001; Villani in J. Stat. Phys. 124:781-822, 2006) and in the econophysical context (Bisi etal. in Commun. Math. Sci. 7:901-916, 2009). Springer Science+Business Media, LLC, 2011 Boltzmann-like equations nationallicence Econophysics nationallicence Granular gases nationallicence Long-time behavior nationallicence Bassetti Federico Dipartimento di Matematica, Università degli Studi di Pavia, via Ferrata 1, 27100, Pavia, Italy aut Ladelli Lucia Dipartimento di Matematica, Politecnico di Milano, P.zza Leonardo da Vinci 32, 20133, Milano, Italy aut Toscani Giuseppe Dipartimento di Matematica, Università degli Studi di Pavia, via Ferrata 1, 27100, Pavia, Italy aut Journal of Statistical Physics Springer US; http://www.springer-ny.com 142/4(2011-02-01), 686-709 0022-4715 142:4<686 2011 142 10955 https://doi.org/10.1007/s10955-011-0136-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-011-0136-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bassetti Federico Dipartimento di Matematica, Università degli Studi di Pavia, via Ferrata 1, 27100, Pavia, Italy aut NATIONALLICENCE 700 1- Ladelli Lucia Dipartimento di Matematica, Politecnico di Milano, P.zza Leonardo da Vinci 32, 20133, Milano, Italy aut NATIONALLICENCE 700 1- Toscani Giuseppe Dipartimento di Matematica, Università degli Studi di Pavia, via Ferrata 1, 27100, Pavia, Italy aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 142/4(2011-02-01), 686-709 0022-4715 142:4<686 2011 142 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer