In this paper, we discuss the large-time behavior of the solution of a simple kinetic model of Boltzmann-Maxwell type, such that the temperature is decreases with time or increases with time. We show that, under the combined effects of the nonlinearity and of the time-monotonicity of the temperature, the kinetic model has nontrivial 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 an 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.

Overpopulated tails in nonconservative kinetic models

PARESCHI, Lorenzo;
2006

Abstract

In this paper, we discuss the large-time behavior of the solution of a simple kinetic model of Boltzmann-Maxwell type, such that the temperature is decreases with time or increases with time. We show that, under the combined effects of the nonlinearity and of the time-monotonicity of the temperature, the kinetic model has nontrivial 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 an 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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/525737
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