# American Institute of Mathematical Sciences

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Stability, convergence to the steady state and elastic limit for the Boltzmann equation for diffusively excited granular media
January  2009, 24(1): 145-157. doi: 10.3934/dcds.2009.24.145

## Boltzmann equation, boundary effects

 1 Institute of Mathematics, Academia Sinica, Taiwan 2 Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore

Received  December 2007 Revised  July 2008 Published  January 2009

The Boltzmann equation, [1], 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.
Citation: Tai-Ping Liu, Shih-Hsien Yu. Boltzmann equation, boundary effects. Discrete & Continuous Dynamical Systems - A, 2009, 24 (1) : 145-157. doi: 10.3934/dcds.2009.24.145
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