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.)
https://hal-polytechnique.archives-ouvertes.fr/hal-00472237
Contributor : François Golse
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Submitted on : Saturday, April 10, 2010 - 8:22:15 AM
Last modification on : Sunday, March 31, 2019 - 1:25:32 AM
Long-term archiving on : Tuesday, September 14, 2010 - 6:22:00 PM
Etienne Bernard, François Golse, Francesco Salvarani. Homogenization of transport problems and semigroups. Mathematical Methods in the Applied Sciences, Wiley, 2010, 33 (10), pp.1228-1234. ⟨10.1002/mma.1319⟩. ⟨hal-00472237⟩
