Inverse Problem for the Wave Equation with a Polynomial Nonlinearity Full article
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Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 , E-ISSN: 1990-4797 |
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| Output data | Year: 2023, Volume: 17, Number: 1, Pages: 163--167 Pages count : 5 DOI: 10.1134/S1990478923010180 | ||||
| Tags | semilinear wave equation, inverse problem, plane wave, X-ray tomography, uniqueness | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0009 |
Abstract:
For the wave equation containing a nonlinearity in the form of an nth order polynomial, we study the problem of determining the coefficients of the polynomial depending on the variable x ∈ R3. We consider plane waves that propagate in a homogeneous medium in the direction of a unit vector ν with a sharp front and incident on an inhomogeneity localized inside a certain ball B(R). It is assumed that the solutions of the problems can be measured at the points of the boundary of this ball at the instants of time close to the arrival of the wavefront for all possible values of the vector ν. It is shown that the solution of the inverse problem is reduced to a series of X-ray tomography problems.
Cite:
Romanov V.G.
, Bugueva T.V.
Inverse Problem for the Wave Equation with a Polynomial Nonlinearity
Journal of Applied and Industrial Mathematics. 2023. V.17. N1. P.163--167. DOI: 10.1134/S1990478923010180 Scopus РИНЦ OpenAlex
Inverse Problem for the Wave Equation with a Polynomial Nonlinearity
Journal of Applied and Industrial Mathematics. 2023. V.17. N1. P.163--167. DOI: 10.1134/S1990478923010180 Scopus РИНЦ OpenAlex
Original:
Романов В.Г.
, Бугуева Т.В.
Обратная задача для волнового уравнения с полиномиальной нелинейностью
Сибирский журнал индустриальной математики. 2023. Т.26. №1. С.142--149. DOI: 10.33048/SIBJIM.2023.26.113 РИНЦ
Обратная задача для волнового уравнения с полиномиальной нелинейностью
Сибирский журнал индустриальной математики. 2023. Т.26. №1. С.142--149. DOI: 10.33048/SIBJIM.2023.26.113 РИНЦ
Dates:
| Submitted: | Oct 31, 2022 |
| Accepted: | Jan 12, 2023 |
| Published print: | May 15, 2023 |
| Published online: | May 15, 2023 |
Identifiers:
| Scopus: | 2-s2.0-85159896233 |
| Elibrary: | 62337693 |
| OpenAlex: | W4376621479 |