Homogenization of transport problems and semigroups

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 integrodifferential 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).