Identification of a localized source in an interstellar cloud: an inverse problem

Lisi, Meri ; Totaro, Silvia

Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 16 (2005) no. 3, pp. 203-209

Résumé

We study an inverse problem for photon transport in an interstellar cloud. In particular, we evaluate the position $x_{0}$ of a localized source $q(x) = q_{0} \delta(x-x_{0})$, 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 of $u$. Because of some monotonic properties of the operator which describes $u$ as a function of $q$, the «position» of the source can be evaluated.