An one-dimensional inverse problem for the wave equation Full article
| Journal |
Eurasian Journal of Mathematical and Computer Applications
ISSN: 2306-6172 , E-ISSN: 2308-9822 |
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| Output data | Year: 2024, Volume: 12, Number: 3, Pages: 135-162 Pages count : 28 DOI: 10.32523/2306-6172-2024-12-3-135-162 | ||||
| Tags | nonlinear wave equation, inverse problem, existence, 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 with inhomogeneity a forward and anone-dimensional inverse problems are studied. The forward problem is considered in the domain x > 0; t > 0 with zero initial data and Dirichlet boundary condition at x = 0. An unique solvability theorem of this problem is proved. The inverse problem is devoted to determining the coefficients under nonlinearities. As an additional information for recovering this coefficients, two forward problems with different Dirichlet data are considered and traces of the derivative of their solutions with respect to x are given at x = 0 on a finite interval. For the inverse problem a local existence and uniqueness theorem is established.
Cite:
Romanov V.G.
, Bugueva T.V.
An one-dimensional inverse problem for the wave equation
Eurasian Journal of Mathematical and Computer Applications. 2024. V.12. N3. P.135-162. DOI: 10.32523/2306-6172-2024-12-3-135-162 WOS Scopus РИНЦ OpenAlex
An one-dimensional inverse problem for the wave equation
Eurasian Journal of Mathematical and Computer Applications. 2024. V.12. N3. P.135-162. DOI: 10.32523/2306-6172-2024-12-3-135-162 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jun 26, 2024 |
| Accepted: | Jul 30, 2024 |
| Published print: | Oct 4, 2024 |
| Published online: | Oct 4, 2024 |
Identifiers:
| Web of science: | WOS:001320677800010 |
| Scopus: | 2-s2.0-85204995039 |
| Elibrary: | 74562464 |
| OpenAlex: | W4403019156 |
Citing:
| DB | Citing |
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| OpenAlex | 2 |