An inverse problem for a nonlinear hyperbolic 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: 2, Pages: 134-154 Pages count : 21 DOI: 10.32523/2306-6172-2024-12-2-134-154 | ||||
| Tags | nonlinear equation, inverse problem, uniqueness, stability estimate. | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0009 |
Abstract:
For a second-order hyperbolic equation with inhomogeneity jujm 1u, m > 1, a forward and an one-dimensional inverse problems are studied. The inverse problem is devoted to determining the coefficient under heterogeneity. As an additional information, the trace of the derivative with respect to x of the solution to the forward initial-boundary value problem is given at x = 0 on a finite interval. Conditions for the unique solvability of the forward problem are found. For the inverse problem a local existence and uniqueness theorems are established and a stability estimate of its solutions is found.
Cite:
Romanov V.G.
, Bugueva T.V.
An inverse problem for a nonlinear hyperbolic equation
Eurasian Journal of Mathematical and Computer Applications. 2024. V.12. N2. P.134-154. DOI: 10.32523/2306-6172-2024-12-2-134-154 WOS Scopus РИНЦ OpenAlex
An inverse problem for a nonlinear hyperbolic equation
Eurasian Journal of Mathematical and Computer Applications. 2024. V.12. N2. P.134-154. DOI: 10.32523/2306-6172-2024-12-2-134-154 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Mar 14, 2024 |
| Accepted: | Apr 16, 2024 |
| Published print: | Jul 2, 2024 |
| Published online: | Jul 2, 2024 |
Identifiers:
| Web of science: | WOS:001272356700009 |
| Scopus: | 2-s2.0-85199415724 |
| Elibrary: | 68769394 |
| OpenAlex: | W4400455627 |