Uniform convergence to equilibrium for granular media

Section 2 is devoted to cases when the convergence is driven by the interaction potential W , with or without exterior potential V : in particular we prove the first result of

However, the study of the non-linear Boltzmann equation for soft potentials without cut-off [ 20 ], and in particular the spectral analysis its linearised version (see for instance [

[1] Kazuo Aoki and Fran¸ cois Golse. On the speed of approach to equilibrium for a colli- sionless gas. On the distribution of free path lengths for the periodic Lorentz gas.

In terms of encoding Dyck paths, inserting a vertex at position k amounts to inserting one up-step followed by one down-step right after time k and slicing at position k amounts

When a number is to be multiplied by itself repeatedly,  the result is a power    of this number.

The framework we choose is that of Gradient Schemes, which has the double benefit of covering a vast number of numerical methods and of having already been studied for many models

Fokker-Planck equation; Granular media equation; Long-time be- haviour; Double-well potential; Free probability; Equilibrium measure; Random ma- trices.. Partial differential

It has been pointed out in a couple of recent works that the weak convergence of its centered and rescaled versions in a weighted Lebesgue L p space, 1 ≤ p < ∞, considered to be