Homogenization of transport problems and semigroups

Etienne Bernard (1, 2) , François Golse (1, 2) , Francesco Salvarani (3)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 LJLL - Laboratoire Jacques-Louis Lions
3 Dipartimento di matematica F. Casorati

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.)

Keywords: Homogenization; Integro-differential equations; Radiative transfer; Opacities

Domains: Mathematics [math]; Analysis of PDEs [math.AP]; Mathematics [math]; Mathematical Physics [math-ph]; Physics [physics]; Mathematical Physics [math-ph]

Etienne Bernard, François Golse, Francesco Salvarani. Homogenization of transport problems and semigroups. Mathematical Methods in the Applied Sciences, 2010, 33 (10), pp.1228-1234. ⟨10.1002/mma.1319⟩. ⟨hal-00472237⟩