Stefan type problem for the generalized Radon transforms in an even-dimensional space

Stefan type problem for the generalized Radon transforms in an even-dimensional space Full article

Journal

Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126

Output data

Year: 2024, Volume: 34, Number: 4, Pages: 261-267 Pages count : 7 DOI: 10.1134/S1055134424040011

Tags

Generalized Radon transform, integral geometry, probing, tomography, differential equation, discontinuous functions.

Authors

Anikonov D.S. ¹ , Konovalova D.S. ¹

Affiliations

1	Sobolev Institute of Mathematics

We study a problem of integral geometry in which functions in variables are integrated over hyperplanes in an-dimensional Euclidean space. We call suchan integration the generalized Radon transform. If the integrand depends only on variables then this integration coincides with the classical one. In a broad sense, the problem of integral geometry is to obtain information about the integrand from the values of a family of integrals. In the present article, we considerthe problem on finding the discontinuity surface of the integrand. We prove that there existsa unique solution of the problem and suggest the corresponding algorithm. It is possible to usethe obtained results in the theory and practice of probing.

Anikonov D.S. , Konovalova D.S.
Stefan type problem for the generalized Radon transforms in an even-dimensional space
Siberian Advances in Mathematics. 2024. V.34. N4. P.261-267. DOI: 10.1134/S1055134424040011 Scopus РИНЦ

Аниконов Д.С. , Коновалова Д.С.
Задача о неизвестной границе для обобщенного преобразования Радона в четно мерном пространстве
Математические труды. 2024. Т.27. №3. С.5–19. DOI: 10.25205/1560-750X-2024-27-3-5-19 РИНЦ

Submitted:	Sep 18, 2024
Accepted:	Oct 30, 2024
Published print:	Jan 14, 2025
Published online:	Jan 14, 2025

Scopus:	2-s2.0-85217406175
Elibrary:	79610850

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