September  2010, 3(3): 395-407. doi: 10.3934/krm.2010.3.395

On a generalized Boltzmann equation for non-classical particle transport

1. 

RWTH Aachen University, Department of Mathematics & Center for Computational Engineering Science, Schinkelstrasse 2, D-52062 Aachen, Germany

2. 

Project-Team SIMPAF–INRIA Lille Nord Europe & Labo. Paul Painlevé CNRS–USTLille, Park Plazza, 40 avenue Halley, F-59650 Villeneuve d’Ascq cedex, France

Received  July 2009 Revised  June 2010 Published  July 2010

We are interested in non-standard transport equations where the description of the scattering events involves an additional "memory variable''. We establish the well posedness and investigate the diffusion asymptotics of such models. While the questions we address are quite classical the analysis is original since the usual dissipative properties of collisional transport equations is broken by the introduction of the memory terms.
Citation: Martin Frank, Thierry Goudon. On a generalized Boltzmann equation for non-classical particle transport. Kinetic & Related Models, 2010, 3 (3) : 395-407. doi: 10.3934/krm.2010.3.395
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