Abstract: A stability estimate for the solution of a source problem for the stationary radiative transfer equation is given. It is supposed that the source has an isotropic distribution. Earlier, stability estimates for this problem were found in a partial case of the emission tomography problem with a vanishing scattering operator and for the complete transfer equation under additional difficult-to-check conditions imposed on the absorption coefficient and the scattering kernel. In this work, we suggest a new fairly 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 of recovering the unknown source, data on solutions of the forward problem related to outgoing radiation are given on a portion of the boundary. The obtained result can be used to estimate the total density of distributed radiation sources.

Cite: Romanov V.G.
A stability estimate in the source problem for the radiative transfer equation
Doklady Mathematics. 2023. V.108. N3. P.450–453. DOI: 10.1134/S106456242370134X WOS Scopus РИНЦ OpenAlex

Original: Романов В.Г.
Оценка устойчивости в задаче об источнике для уравнения переноса излучения
Доклады Академии наук. Серия: Математика, информатика, процессы управления. 2023. Т.514. №1. С.34-38. DOI: 10.31857/S2686954323600271 РИНЦ OpenAlex

Dates:

Submitted:	May 10, 2023
Accepted:	Oct 18, 2023
Published print:	Dec 27, 2023
Published online:	Mar 7, 2024

Identifiers:

Web of science:	WOS:001184111000010
Scopus:	2-s2.0-85187909492
Elibrary:	65119010
OpenAlex:	W4392824545

Citing: Пока нет цитирований

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