AN STABILITY ESTIMATE IN 3D SOURCE PROBLEM FOR THE STATIONARY RADIATIVE TRANSFER EQUATION

Abstract

It is given a stability estimate of a solution of a source problem for the stationary radiative transfer equation. It is suppose that the source is an isotropic distribution. Earlier stability estimates for this problem were studied in several papers, the most part of those was related to a partial case of the emission tomography problem, when the scattering operator vanishes. For the complete transfer equation the stability estimate were given under additional conditions for the absorption coefficient and the scattering kernel, those are sufficiently difficult for checking. Moreover, it is still open the question about dependence a constant in the stability estimate on the coefficients of the transfer equation. In the present work, the stationary transfer equation is considered in an compact strongly convex domain of the tree-dimension space. In a forward problem it is assumed that incoming radiation is absent. In an inverse problem for recovering an unknown source some data for solutions of the forward problem are given. A new simple approach is suggested to obtain a stability estimate for the problem under the consideration. Using this way, an explicit constant in this estimate is given.