Self-similarity and power-like tails in nonconservative kinetic models

Details Self-similarity and power-like tails in nonconservative kinetic models Self-similarity and power-like tails in nonconservative kinetic models

2010-09-14

arxiv.org/abs/1009.2760v1

Journal of Statistical Physics, 124 (2006), 747-779

Mathematics

Analysis of PDEs

Scientific paper

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.

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