An inverse problem for a nonlinear wave equation with damping Full article
| Journal |
Eurasian Journal of Mathematical and Computer Applications
ISSN: 2306-6172 , E-ISSN: 2308-9822 |
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| Output data | Year: 2023, Volume: 11, Number: 2, Pages: 99-115 Pages count : 17 DOI: 10.32523/2306-6172-2023-11-2-99-115 | ||
| Tags | nonlinear wave equations, point source, inverse problem, tomography, integral geomety | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0009 |
Abstract:
We consider an inverse problem of recovering two coefficients in a semi-linear wave equation. This equation contains a damping term and a term with a quadratic nonlinearity. The inverse problem consists in recovering coefficients under these terms as function of the space variable x 2 R3. A forward problem for the equation with a point source is studied. As a result, the inverse problem reduce to two problems, one of them is the well known problem of X-ray tomography, the other one is the problem of the integral geometry with a with a special weight function. The latter problem is studied and a stability estimate for the solution of this problem is stated.
Cite:
Romanov V.G.
An inverse problem for a nonlinear wave equation with damping
Eurasian Journal of Mathematical and Computer Applications. 2023. V.11. N2. P.99-115. DOI: 10.32523/2306-6172-2023-11-2-99-115 WOS Scopus РИНЦ OpenAlex
An inverse problem for a nonlinear wave equation with damping
Eurasian Journal of Mathematical and Computer Applications. 2023. V.11. N2. P.99-115. DOI: 10.32523/2306-6172-2023-11-2-99-115 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Mar 20, 2023 |
| Accepted: | Apr 17, 2023 |
| Published print: | Jun 8, 2023 |
| Published online: | Jun 8, 2023 |
Identifiers:
| Web of science: | WOS:001015856900005 |
| Scopus: | 2-s2.0-85162109622 |
| Elibrary: | 61811708 |
| OpenAlex: | W4383113693 |
Citing:
| DB | Citing |
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| Scopus | 1 |