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Homogenization of transport problems and semigroups

✍ Scribed by Etienne Bernard; François Golse; Francesco Salvarani

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
161 KB
Volume
33
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

In some cases, the homogenization of evolution differential equations whose solution is given by the action of a semigroup on their initial data may lead to evolution problems with a completely different structure, usually integro‐differential equations whose dynamics is not defined by a semigroup, but involves memory effects. A typical example is the homogenization—or discretization—of opacities in radiative transfer. In this paper, we propose a formulation of homogenized equations in terms of a semigroup acting on an enlarged phase space (i.e. on functions involving more variables than in the original problem). Copyright © 2010 John Wiley & Sons, Ltd.

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