THE GRAZING COLLISIONS ASYMPTOTICS OF THE NON CUTOFF KAC EQUATION

We investigate the non cut-off-Kac equation when the cross-section is concentrating on grazing collisions. We prove that this process leads to the one-dimensional Fokker-Planck equation, and that, at last under suitable regularity of the initial data, the convergence is uniform i n time. (C) Elsevier, Paris.