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Identification of a localized source in an interstellar cloud: an inverse problem. (English) Zbl 1225.82059

Summary: 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 quasistatic 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.

MSC:

82C70 Transport processes in time-dependent statistical mechanics
35R30 Inverse problems for PDEs
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