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In this paper, we study a one-dimensional mathematical model for a contracting interstellar cloud, with a star inside. Existence and uniqueness of a positive solution are proved by means of the fixed point theorem. A time discretization procedure is given and the case of an expanding interstellar cloud is also considered.

We study an inverse problem for photon transport in an interstellar cloud. In particular, we evaluate the position $x_0$ of a localized source $q\left(x\right)=q_0\delta \left(x-x_0\right)$, inside a nebula (for example, a star). We assume that the photon transport phenomenon is one-dimensional. Since a nebula moves slowly in time, the number of photons $U$ inside the cloud changes slowly in time. For this reason, we consider the so-called quasi-static approximation $u$ to the exact solution $U$. By using semigroup theory, we prove existence and uniqueness...