An Inverse Source Problem in Radiative Transfer with Partial Data

Details An Inverse Source Problem in Radiative Transfer with Partial Data An Inverse Source Problem in Radiative Transfer with Partial Data

2011-05-09

arxiv.org/abs/1105.1577v3

Mathematics

Analysis of PDEs

27 pages, 2 figures, accepted to Inverse Problems

Scientific paper

The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a certain subset of the domain, which we call the visible set. Furthermore, it is shown for an open dense set of $C^{\infty}$ absorption and scattering coefficients that one can recover the part of the wave front set of the source that is supported in the microlocally visible set, modulo a function in the Sobolev space $H^{k}$ for $k$ arbitrarily large. This is an extension to the full data case, which is considered in \cite{inversesource}.

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