caa a22 4500 467891346 CHVBK 20180406152750.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s10955-006-9025-y doi (NATIONALLICENCE)springer-10.1007/s10955-006-9025-y Self-Similarity and Power-Like Tails in Nonconservative Kinetic Models [Elektronische Daten] [Lorenzo Pareschi, Giuseppe Toscani] In this paper, we discuss the large-time behavior of solution of a simple kinetic model of Boltzmann-Maxwell type, such that the temperature is time decreasing and/or time increasing. We show that, under the combined effects of the nonlinearity and of the time-monotonicity of the temperature, the kinetic model has non trivial quasi-stationary states with power law tails. In order to do this we consider a suitable asymptotic limit of the model yielding a Fokker-Planck equation for the distribution. The same idea is applied to investigate the large-time behavior of an elementary kinetic model of economy involving both exchanges between agents and increasing and/or decreasing of the mean wealth. In this last case, the large-time behavior of the solution shows a Pareto power law tail. Numerical results confirm the previous analysis. Springer Science + Business Media, Inc., 2006 Granular gases nationallicence overpopulated tails nationallicence Boltzmann equation nationallicence wealth and income distributions nationallicence Pareto distribution nationallicence Pareschi Lorenzo Department of Mathematics and Center for Modelling Computing and Statistics (CMCS), University of Ferrara, Via Machiavelli 35, I-44100, Ferrara, Italy aut Toscani Giuseppe Department of Mathematics, University of Pavia, via Ferrata 1, 27100, Pavia, Italy aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 747-779 0022-4715 124:2-4<747 2006 124 10955 https://doi.org/10.1007/s10955-006-9025-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9025-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Pareschi Lorenzo Department of Mathematics and Center for Modelling Computing and Statistics (CMCS), University of Ferrara, Via Machiavelli 35, I-44100, Ferrara, Italy aut NATIONALLICENCE 700 1- Toscani Giuseppe Department of Mathematics, University of Pavia, via Ferrata 1, 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), 747-779 0022-4715 124:2-4<747 2006 124 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer