An inverse problem for a nonlinear transport equation Full article
| Journal |
Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2024, Volume: 65, Number: 5, Pages: 1195-1200 Pages count : 6 DOI: 10.1134/S0037446624050185 | ||
| Tags | nonlinear transport equation, inverse problem, tomography, uniqueness | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0009 |
Abstract:
Under consideration is a nonlinear transport equation containing two nonlinearities and a coefficient q(x) of a lower-order nonlinear term depending on two or three space variables. We study the direct problem with the data on a part of the lateral surface of a cylindrical domain, explicitly construct a solution, and prove the uniqueness of the solution. Also, we state the problem of recovering the coefficient q(x) on some information about a solution to the direct problem and demonstrate that the inverse problem reduces to an X-ray tomography problem. This opens a way to its efficient numerical solution.
Cite:
Romanov V.G.
An inverse problem for a nonlinear transport equation
Siberian Mathematical Journal. 2024. V.65. N5. P.1195-1200. DOI: 10.1134/S0037446624050185 WOS Scopus РИНЦ OpenAlex
An inverse problem for a nonlinear transport equation
Siberian Mathematical Journal. 2024. V.65. N5. P.1195-1200. DOI: 10.1134/S0037446624050185 WOS Scopus РИНЦ OpenAlex
Original:
Романов В.Г.
Обратная задача для нелинейного уравнения переноса
Сибирский математический журнал. 2024. Т.65. №5. С.1022-1028. DOI: 10.33048/smzh.2024.65.518 РИНЦ
Обратная задача для нелинейного уравнения переноса
Сибирский математический журнал. 2024. Т.65. №5. С.1022-1028. DOI: 10.33048/smzh.2024.65.518 РИНЦ
Dates:
| Submitted: | Jul 29, 2024 |
| Accepted: | Aug 20, 2024 |
| Published print: | Sep 20, 2024 |
| Published online: | Sep 20, 2024 |
Identifiers:
| Web of science: | WOS:001320442300010 |
| Scopus: | 2-s2.0-85204772354 |
| Elibrary: | 69920894 |
| OpenAlex: | W4402842354 |