Nonlinear Problems in the Kinetic Theory of Gases

Abstract

In the previous meeting of this series, held in Bad Honnef. I presented a survey lecture on “Half-space Problems in the Kinetic Theory of Gases” [1]. In the concluding remarks of that paper, I pointed out that it was not hopeless to try to obtain new results for nonlinear boundary value problems in kinetic theory. I am glad to report that there has been progress in this direction. It is for this reason that, although there are interesting new results on the initial value problem for nonlinear kinetic equations [2–4]. I shall be dealing here with the recent progress on boundary value problems for nonlinear kinetic equations. These results refer to discrete velocity models and are the outcome of my Joint work with R. Illner and the late Marvin Shinbrot [5,6]. A more recent result, obtained in collaboration with these authors and M. Pulvirenti [7] deals with half-space problems and is thus directly related to my survey [1].