The grazing collisions asymptotics of the non cut-off Kac equation
نویسنده
چکیده
— We investigate the non cut-off Kac équation when the cross-section is concentrating on grazing collisions. We prove that this process leads to the one-dimensional Fokker-Planck équation, and that, at last under suitable regularity of the initial data, the convergence is uniform in time. © Elsevier, Paris Résumé. — On s'intéresse à l'équation de Kac « non cut-off» lorsque la section transversale se concentre sur les collisions rasantes. On montre que l'on aboutit à l'équation de Fokker-Planck en dimension 1 d'espace, et que sous des hypothyses de régularité de la donnée initiale, il y a convergence uniforme en temps. © Elsevier, Paris
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