This issuePrevious ArticleOn cooperative parabolic systems: Harnack inequalities and asymptotic symmetryNext ArticleStability,
convergence to the steady state and elastic limit for the Boltzmann
equation for diffusively excited granular media
The Boltzmann equation, , offers richer and physically more realistic modelling of the boundary effects than the fluid dynamic equations. Important phenomena such as the thermal transpiration and some of the bifurcations due to curvature of the boundary can only modeled using the kinetic formulation. In this paper we survey the analytical ideas that have been introduced in recent years for the study of the boundary effects. The main point is that more quantitative estimates of the solutions are needed for such a study.