On a generalized Boltzmann equation for non-classical particle transport

Martin Frank; Thierry Goudon

doi:10.3934/krm.2010.3.395

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2010, Volume 3, Issue 3: 395-407. Doi: 10.3934/krm.2010.3.395

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On a generalized Boltzmann equation for non-classical particle transport

Martin Frank^1, and
Thierry Goudon^2,

1.
RWTH Aachen University, Department of Mathematics & Center for Computational Engineering Science, Schinkelstrasse 2, D-52062 Aachen
2.
Project-Team SIMPAF–INRIA Lille Nord Europe & Labo. Paul Painlevé CNRS–USTLille, Park Plazza, 40 avenue Halley, F-59650 Villeneuve d’Ascq cedex

Received: July 2009

Revised: June 2010

Published: September 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q99; Secondary: 35B25, 82C70.

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