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arXiv · 1009.2760

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

L. Pareschi·G. Toscani
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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.

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BibTeXRIS

L. Pareschi, G. Toscani. 2010-09-14. Self-similarity and power-like tails in nonconservative kinetic models. https://doi.org/10.1007/s10955-006-9025-y

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