Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Averaging lemmas without time Fourier transform and application to discretized kinetic equations

F. Bouchuta1 and L. Desvillettesa2

a1 Université d'Orléans et CNRS, UMR 6628, Département de Mathématiques, BP 6759, 45067 Orléans cedex 2, France fbouchut@labomath.univ-orleans.fr

a2 Université d'Orléans et CNRS, UMR 6628, Département de Mathématiques, BP 6759, 45067 Orléans cedex 2, France desville@labomath.univ-orleans.fr

We prove classical averaging lemmas in the L2 framework with the help of the Fourier transform in variables x and v, but not t. This method is then used to study discretized problems arising out of the numerical analysis of kinetic equations.

(Received July 31 1997)