Moment Inequalities and High-Energy Tails for Boltzmann Equations with Inelastic Interactions
نویسندگان
چکیده
We study the high-energy asymptotics of the steady velocity distributions for model systems of granular media in various regimes. The main results obtained are integral estimates of solutions of the hard-sphere Boltzmann equations, which imply that the velocity distribution functions f(v) behave in a certain sense as C exp(−r|v|s) for |v| large. The values of s, which we call the orders of tails, range from s = 1 to s = 2, depending on the model of external forcing. The method we use is based on the moment inequalities and careful estimating of constants in the integral form of the Povzner-type inequalities.
منابع مشابه
Moment Inequalities and High-energy Tails for the Boltzmann Equations with Inelastic Interactions
We study the high-energy asymptotics of the steady velocity distributions for model systems of granular media in various regimes. The main results obtained are integral estimates of solutions of the hard-sphere Boltzmann equations, which imply that the velocity distribution functions f(v) behave in a certain sense as C exp(−r|v|s) for |v| large. The values of s, which we call the orders of tail...
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