A Hölder stability estimate for a 3D coefficient inverse problem for a hyperbolic equation with a plane wave Full article
| Journal |
Journal of Inverse and Ill-Posed Problems
ISSN: 0928-0219 , E-ISSN: 1569-3945 |
||||
|---|---|---|---|---|---|
| Output data | Year: 2022, DOI: 10.1515/jiip-2022-0071 | ||||
| Tags | Carleman estimate; Coefficient inverse problem; geodesic lines; hyperbolic equation; Hölder stability estimate | ||||
| Authors |
|
||||
| Affiliations |
|
Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0009 |
Abstract:
Abstract. A 3D coefficient inverse problem for a hyperbolic equation with non-overdetermined data is considered. The forward problem is the Cauchy problem with the initial condition being the delta function concentrated at a single plane (i.e. the plane wave). A certain associated operator is written in finite differences with respect to two out of three spatial variables, i.e. “partial finite differences”. The grid step size is bounded from below by a fixed number. A Carleman estimate is applied to obtain, for the first time, a Hölder stability estimate for this problem. Another new result is an estimate from below the amplitude of the first term of the expansion of the solution of the forward problem near the characteristic wedge.
Cite:
Klibanov M.V.
, Romanov V.G.
A Hölder stability estimate for a 3D coefficient inverse problem for a hyperbolic equation with a plane wave
Journal of Inverse and Ill-Posed Problems. 2022. DOI: 10.1515/jiip-2022-0071 WOS Scopus РИНЦ OpenAlex
A Hölder stability estimate for a 3D coefficient inverse problem for a hyperbolic equation with a plane wave
Journal of Inverse and Ill-Posed Problems. 2022. DOI: 10.1515/jiip-2022-0071 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Sep 8, 2022 |
| Accepted: | Sep 27, 2022 |
| Published online: | Nov 24, 2022 |
| Published print: | Apr 1, 2023 |
Identifiers:
| Web of science: | WOS:000889253800001 |
| Scopus: | 2-s2.0-85143067642 |
| Elibrary: | 57721968 |
| OpenAlex: | W4309827591 |