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.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
