A STABILITY ESTIMATE IN THE SOURCE PROBLEM FOR THE RADIATIVE TRANSFER EQUATION-Reference-Cited by-同舟云学术

A STABILITY ESTIMATE IN THE SOURCE PROBLEM FOR THE RADIATIVE TRANSFER EQUATION

Published:2023-11-01 Issue:1 Volume:514 Page:34-38
ISSN:2686-9543
Container-title:Доклады Российской академии наук. Математика, информатика, процессы управления
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Short-container-title:Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ

Author:

Romanov V. G.¹

Affiliation:

1. Sobolev Institute of Mathematics

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 known in a partial case of the emission tomography problem only, when the scattering operator vanishes, and for the complete transfer equation under additional and difficult in checking conditions for the absorption coefficient and the scattering kernel. In the present work, we suggest a new and enough simple approach for obtaining a stability estimate for the problem under the consideration. The transfer equation is considered in a circle of the two-dimension space. In the forward problem, it is assumed that incoming radiation is absent. In the inverse problem for recovering the unknown source some data for solutions of the forward problem related to outgoing radiation are given. The obtained result can be used for an estimation of the summary density of distributed sources of the radiation.

Publisher

The Russian Academy of Sciences

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