Homogenization of transport problems and semigroups
Étienne Bernard, François Golse, Francesco Salvarani · Mathematical Methods in the Applied Sciences · 2010
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.