Physics – Mathematical Physics
Scientific paper
2003-06-03
Physics
Mathematical Physics
22 pages
Scientific paper
10.1023/B:JOSS.0000041751.11664.
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 {\em 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.
Bobylev Alexander V.
Gamba Irene M.
Panferov Vladislav A.
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