Inverse problem for a nonlinear wave equation Full article
| Journal |
Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 , E-ISSN: 1990-4797 |
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| Output data | Year: 2022, Volume: 16, Number: 2, Pages: 333–348 Pages count : DOI: 10.1134/S1990478922020132 | ||||
| Tags | nonlinear wave equation, inverse problem, integral geometry | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0009 |
Abstract:
We consider the inverse problem of determining the coefficient of the nonlinear term in an equation whose main part is the wave operator. The properties of the solution of the direct problem are studied; in particular, the existence and uniqueness of a bounded solution in a neighborhood of the characteristic cone is established, and the structure of this solution is written out. The problem of finding the unknown function is reduced to the problem of integral geometry on a family of straight lines with a weight function invariant with respect to rotations around some fixed point. The uniqueness of the solution of the inverse problem is established, and an algorithm for reconstructing the desired function is proposed.
Cite:
Romanov V.G.
, Bugueva T.V.
Inverse problem for a nonlinear wave equation
Journal of Applied and Industrial Mathematics. 2022. V.16. N2. P.333–348. DOI: 10.1134/S1990478922020132 Scopus РИНЦ OpenAlex
Inverse problem for a nonlinear wave equation
Journal of Applied and Industrial Mathematics. 2022. V.16. N2. P.333–348. DOI: 10.1134/S1990478922020132 Scopus РИНЦ OpenAlex
Original:
Романов В.Г.
, Бугуева Т.В.
Обратная задача для нелинейного волнового уравнения
Сибирский журнал индустриальной математики. 2022. Т.25. №2. С.83-100. DOI: 10.33048/SIBJIM.2022.25.206 РИНЦ
Обратная задача для нелинейного волнового уравнения
Сибирский журнал индустриальной математики. 2022. Т.25. №2. С.83-100. DOI: 10.33048/SIBJIM.2022.25.206 РИНЦ
Dates:
| Submitted: | Dec 16, 2021 |
| Accepted: | Jan 13, 2022 |
| Published print: | Nov 15, 2022 |
| Published online: | Nov 15, 2022 |
Identifiers:
| Scopus: | 2-s2.0-85141917191 |
| Elibrary: | 51788432 |
| OpenAlex: | W4312518602 |