A photon transport problem with a time-dependent point source

We consider a time-dependent problem of photon transport in an interstellar cloud with a point photon source modeled by a Dirac δ functional. The existence of a unique distributional solution to this problem is established by using the theory of continuous semigroups of operators on locally convex spaces coupled with a constructive approach for producing spaces of generalized functions

Kinetic models for dust coagulation in interstellar clouds

In this paper we propose some kinetic models which take into account different mechanisms of coagulation between two populations of dust particles inside in-terstellar nebulae, and we discuss their mathematical properties. These models are in general nonlinear; however, at the end of the paper we perform an ap-proximate procedure to obtain a linear transport equation even for the model which considers the most general mechanism of coagulation.