Moment Inequalities and High-Energy Tails for Boltzmann Equations with Inelastic Interactions

By A. Bobylev, Irene M. Gamba, V. Panferov. 2003

136 citations recorded by the source corpus.

We study high-energy asymptotics of the steady velocity distributions for model kinetic equations describing various regimes in dilute granular flows. The main results obtained are integral estimates of solutions of the Boltzmann equation for inelastic hard spheres, which imply that steady velocity distributions 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. To obtain these results we establish precise estimates for exponential moments of solutions, using a sharpened version of the Povzner-type inequalities.

Subfields: Applied Mathematics, Computational Mechanics, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/59e6a5cd498cf15485bb4922ac633d37eadde5a3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Mechanics

In Ocean Engineering

Citations in the corpus

Factorization for non-symmetric operators and exponential H-theorem (2010, methodology): “s estimates are now a classical tool in the theory of the spatially homogeneous Boltzmann equation. Exponential moments estimates for the spatially homogeneous Boltzmann equation are more recent, see [16, 18, 41] and the references therein. In the latter references exponential moments (in integral o”
On the Boltzmann Equation for Diffusively Excited Granular Media (2003, background): “As a general rule, the exponents in the tails are expected to depend on the driving and collision mechanisms [2, 16, 17, 7 ]. In fact, deviations of the steady states of granular systems from Maxwellian equilibria (\thickening of tails") is one of the characteristic features of dynamics of granular”
Rate of Convergence to Equilibrium for the Spatially Homogeneous Boltzmann Equation with Hard Potentials (2006, background): “C13 kg0kL1 e −µt. This concludes the proof since kgtkL1 = kft −MkL1(m−1). Finally we need a result on the appearance and propagation of the L1(m−1) norm. This lemma is a variant of results in [5] and [8], and it is a particular case of more general results in [27]. 42 CLEMENT MOUHOT´ Lemma 4.7. Let ”