Time dependent photon transport in a three dimensional interstellar cloud with stochastic clumps

Abstract

We consider time dependent photon transport in a three dimensional interstellar cloud which occupies a three dimensional regionV. One or more clumps of given shapes are present withinV and their positions are determined by a suitable set of stochastic variables. Iff is the photon number density in the cloud or in the clumps, then our mathematical model leads to two coupled initial value problems for the average photon density over the stochastic variables 〈f〉 and forf* =f -〈f〉. By using the theory of semigroups, we prove existence and uniqueness of a strongly continuous solution and examine the small fluctuation approximation of such a solution.