Self-similarity and power-like tails in nonconservative kinetic models
Abstract
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.
Keywords
Cite
@article{arxiv.1009.2760,
title = {Self-similarity and power-like tails in nonconservative kinetic models},
author = {L. Pareschi and G. Toscani},
journal= {arXiv preprint arXiv:1009.2760},
year = {2015}
}