An inverse problem for the wave equation with nonlinear damping Full article
| Journal |
Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2023, Volume: 64, Number: 3, Pages: 670–685 Pages count : 16 DOI: 10.1134/S003744662303014X | ||
| Tags | nonlinear wave equation, inverse problem, existence of solutions, stability estimate | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 |
Министерство науки и высшего образования РФ Mathematical Center in Akademgorodok |
075-15-2019-1613, 075-15-2022-281 |
Abstract:
We study the inverse problem of recovering a coefficient at the nonlinearity in a second order hyperbolic equation with nonlinear damping. The unknown coefficient depends on one space variable x. Also, we consider the process of wave propagation along the semiaxis x > 0 given the derivative with respect to x at x = 0. As additional information in the inverse problem we consider the trace of a solution to the initial boundary value problem on a finite segment of the axis x = 0 and find the conditions for unique solvability of the direct problem. We also establish a local existence theorem and a global stability estimate for a solution to the inverse problem.
Cite:
Romanov V.G.
An inverse problem for the wave equation with nonlinear damping
Siberian Mathematical Journal. 2023. V.64. N3. P.670–685. DOI: 10.1134/S003744662303014X WOS Scopus РИНЦ OpenAlex
An inverse problem for the wave equation with nonlinear damping
Siberian Mathematical Journal. 2023. V.64. N3. P.670–685. DOI: 10.1134/S003744662303014X WOS Scopus РИНЦ OpenAlex
Original:
Романов В.Г.
Обратная задача для волнового уравнения с нелинейным поглощением
Сибирский математический журнал. 2023. Т.64. №3. С.635-652. DOI: 10.33048/smzh.2023.64.314 РИНЦ
Обратная задача для волнового уравнения с нелинейным поглощением
Сибирский математический журнал. 2023. Т.64. №3. С.635-652. DOI: 10.33048/smzh.2023.64.314 РИНЦ
Dates:
| Submitted: | Mar 9, 2023 |
| Accepted: | Apr 6, 2023 |
| Published print: | May 24, 2023 |
| Published online: | May 24, 2023 |
Identifiers:
| Web of science: | WOS:000996393600014 |
| Scopus: | 2-s2.0-85159925767 |
| Elibrary: | 61519392 |
| OpenAlex: | W4377990862 |