The problem of the simultaneous determination of the attenuation factor and scattering indicatrix for the stationary transfer equation (Q1386561)

The inverse problems of the determination of coefficients and special right-hand sides of the transfer equation were considered earlier. In this work, we study the problem of the simultaneous determination of the attenuation factor \(\sigma(x)\), \(x\in\mathbb{R}^3\) and scattering indicatrix \(K(x,v\cdot v')\) by the output radiation that is given on the boundary of the domain. The peculiar feature of the formulation in question is the presence of radiation concentrated with respect to the angular variables. A similar statement of the problem was previously investigated by the author for the case of the two-dimensional space \((x\in\mathbb{R}^2)\). The transition from the two-dimensional space to the three-dimensional space turns out to be nontrivial, as it frequently is, and requires special consideration, the results of which are adduced in the paper.