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Stability estimates in problems of recovering the attenuation coefficient and the scattering indicatrix for the transport equation. (English) Zbl 0860.35146

Summary: We consider two inverse problems for a stationary transport equation. The first is the problem of simultaneous reconstruction of the attenuation coefficient and the density of sources distributed in a domain \(D\subset \mathbb{R}^3\) under the assumption that the scattering kernel is known. Two observations are used for reconstructing unknown functions. The second problem is to recover simultaneously the attenuation coefficient and the scattering kernel using information on outgoing radiation at the boundary of the domain \(D\) which corresponds to a sharply directed incident radiation.
If attenuation and scattering are sufficiently small, stability estimates for both problems are obtained.

MSC:

35R30 Inverse problems for PDEs
35Q72 Other PDE from mechanics (MSC2000)
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