An inverse problem for the wave equation with two nonlinear terms Full article
| Journal |
Differential Equations
ISSN: 0012-2661 , E-ISSN: 1608-3083 |
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| Output data | Year: 2024, Volume: 60, Number: 4, Pages: 479–491 Pages count : 13 DOI: 10.1134/S0012266124040074 | ||
| Tags | inverse problem, nonlinear equation, integral geometry, uniqueness, stability | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0009 |
Abstract:
An inverse problem for a second-order hyperbolic equation containing two nonlinear terms is studied. The problem is to reconstruct the coefficients of the nonlinearities. The Cauchy problem with a point source located at a point y is considered. This point is a parameter of the problem and successively runs over a spherical surface S. It is assumed that the desired coefficients are nonzero only in a domain lying inside S. The trace of the solution of the Cauchy problem on S is specified for all possible values of y and for times close to the arrival of the wave from the source to the points on the surface S; this allows reducing the inverse problem under consideration to two successively solved problems of integral geometry. Solution stability estimates are found for these two problems.
Cite:
Romanov V.G.
An inverse problem for the wave equation with two nonlinear terms
Differential Equations. 2024. V.60. N4. P.479–491. DOI: 10.1134/S0012266124040074 WOS Scopus РИНЦ OpenAlex
An inverse problem for the wave equation with two nonlinear terms
Differential Equations. 2024. V.60. N4. P.479–491. DOI: 10.1134/S0012266124040074 WOS Scopus РИНЦ OpenAlex
Original:
Романов В.Г.
Обратная задача для волнового уравнения с двумя нелинейными членами
Дифференциальные уравнения. 2024. V.60. N4. P.508-520. DOI: 10.31857/s0374064124040061 РИНЦ OpenAlex
Обратная задача для волнового уравнения с двумя нелинейными членами
Дифференциальные уравнения. 2024. V.60. N4. P.508-520. DOI: 10.31857/s0374064124040061 РИНЦ OpenAlex
Dates:
| Submitted: | Feb 1, 2024 |
| Accepted: | Feb 13, 2024 |
| Published print: | Jul 23, 2024 |
| Published online: | Jul 23, 2024 |
Identifiers:
| Web of science: | WOS:001280829900010 |
| Scopus: | 2-s2.0-85200044483 |
| Elibrary: | 68537844 |
| OpenAlex: | W4401106013 |