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Homogenisation of transport kinetic equations with oscillating potentials

Published online by Cambridge University Press:  14 November 2011

E. Frenod  and
K. Hamdache
E. Frenod
Affiliation:
CMLA, ENS Cachan, URA CNRS 1161, 61 avenue du Président Wilson, F-94235 Chachan Cedex, France
K. Hamdache
Affiliation:
MAB, CNRS/Université de Bordeaux I, 351 cours de la libération, F-33405 Talence Cedex, France
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Abstract

We consider the homogenisation of transport kinetic equations with a highly periodic oscillating external field. The external field, acting on the particles, consists of a sum of a field deriving from a periodic potential and a bounded periodic perturbation. For the profile function generated by the oscillating solution of the problem, we derive a kinetic model with transmission boundary conditions in the energy variable. In some cases, for example when the field is not perturbed, we deduce a transport kinetic equation with memory effect satisfied by the weak-* limit of the sequence of solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 6 , 1996 , pp. 1247 - 1275
Copyright
Copyright © Royal Society of Edinburgh 1996

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