Sharafutdinov, V. A. An inverse problem of determining a source in the stationary transport equation for a medium with refraction. (English. Russian original) Zbl 0851.53046 Sib. Math. J. 35, No. 4, 835-843 (1994); translation from Sib. Mat. Zh. 35, No. 4, 937-945 (1994). Summary: We consider the problem of finding the source distribution for particles (or radiation) in a bounded domain \(D\) from the outgoing flow through the boundary of \(D\). The domain \(D\) is filled with a medium that influences the particles trifold: first, the medium absorbs the particles; second, it scatters them; third, it bends the particle trajectories so that, between two scattering acts, a particle moves with unit velocity along a geodesic of some Riemannian metric. The medium is assumed to be known; i.e., the absorption, scattering diagram, and Riemannian metric are given. We obtain uniqueness for a solution to the problem and a stability estimate under certain assumptions of smallness of the absorption, scattering diagram, and curvature of the metric. Cited in 13 Documents MSC: 53Z05 Applications of differential geometry to physics 82C70 Transport processes in time-dependent statistical mechanics 85A25 Radiative transfer in astronomy and astrophysics 45G10 Other nonlinear integral equations Keywords:geodesic flow; source distribution for particles; absorption; scattering diagram; Riemannian metric; stability estimate; curvature PDFBibTeX XMLCite \textit{V. A. Sharafutdinov}, Sib. Math. J. 35, No. 4, 835--843 (1994; Zbl 0851.53046); translation from Sib. Mat. Zh. 35, No. 4, 937--945 (1994) Full Text: DOI References: [1] V. A. Sharafutdinov, ”A tomography emission problem for inhomogeneous media,” Dokl. RAN,326, No. 3, 446–448 (1992). [2] V. A. Sharafutdinov, Integral Geometry of Tensor Fields [in Russian], Nauka, Novosibirsk (1993). · Zbl 0795.53070 [3] L. P. Einsenhart, Riemannian Geometry [Russian translation], Izdat. Inostr. Lit., Moscow (1948). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.