TIME-DEPENDENT PHOTON TRANSPORT IN A 3-DIMENSIONAL INTERSTELLAR CLOUDWITH STOCHASTIC CLUMPS

We consider time dependent photon transport in a three dimensional int erstellar cloud which occupies a three dimensional region V. One or mo re clumps of given shapes are present within V and their positions are determined by a suitable set of stochastic variables. If f is the pho ton number density in the cloud or in the clumps, then our mathematica l model leads to two coupled initial value problems for the average ph oton density over the stochastic variables [f] and for f = f - [f]. B y using the theory of semigroups, we prove existence and uniqueness of a strongly continuous solution and examine the small fluctuation appr oximation of such a solution.