One-Dimensional Inverse Problem for Nonlinear Equations of Electrodynamics Full article
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Differential Equations
ISSN: 0012-2661 , E-ISSN: 1608-3083 |
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| Output data | Year: 2023, Volume: 59, Number: 10, Pages: 1397-1412 Pages count : 16 DOI: 10.1134/s00122661230100075 | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0009 |
Abstract:
For the system of nonlinear electrodynamics equations, we consider the problem of determining the medium conductivity coefficient multiplying the nonlinearity. It is assumed that the permittivity and permeability are constant and the conductivity depends only on one spatial variable x, with this conductivity being zero on the half-line x < 0. For a mode in which only two electromagnetic field components participate, the wave propagation process caused by the incidence of a plane wave with a constant amplitude from the domain x < 0 onto an inhomogeneity localized on the half-line x ≥ 0 is considered. With a given conductivity coefficient, the conditions for the solvability of the direct problem and the properties of its solution are studied. To solve the inverse problem, the trace of the electrical component of the solution of the direct problem is specified on a finite segment of the axis x = 0. A theorem on the local existence and uniqueness of the solution of the inverse problem is established, and a global estimate of the conditional stability of its solutions is found.
Cite:
Romanov V.G.
One-Dimensional Inverse Problem for Nonlinear Equations of Electrodynamics
Differential Equations. 2023. V.59. N10. P.1397-1412. DOI: 10.1134/s00122661230100075 WOS Scopus РИНЦ OpenAlex
One-Dimensional Inverse Problem for Nonlinear Equations of Electrodynamics
Differential Equations. 2023. V.59. N10. P.1397-1412. DOI: 10.1134/s00122661230100075 WOS Scopus РИНЦ OpenAlex
Original:
Романов В.Г.
Одномерная обратная задача для нелинейных уравнений электродинамики
Дифференциальные уравнения. 2023. Т.59. №10. С.1397-1411. DOI: 10.31857/S0374064123100072 РИНЦ OpenAlex
Одномерная обратная задача для нелинейных уравнений электродинамики
Дифференциальные уравнения. 2023. Т.59. №10. С.1397-1411. DOI: 10.31857/S0374064123100072 РИНЦ OpenAlex
Dates:
| Submitted: | Jul 14, 2023 |
| Accepted: | Aug 25, 2023 |
| Published print: | Nov 27, 2023 |
| Published online: | Nov 27, 2023 |
Identifiers:
| Web of science: | WOS:001109970300007 |
| Scopus: | 2-s2.0-85178270735 |
| Elibrary: | 64413314 |
| OpenAlex: | W4388934556 |