On an Inverse Dynamic Problem for the Wave Equation with a Potential on a Real Line
- Authors: Mikhaylov A.S.1, Mikhaylov V.S.1
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Affiliations:
- St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg State University
- Issue: Vol 238, No 5 (2019)
- Pages: 701-714
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242588
- DOI: https://doi.org/10.1007/s10958-019-04268-z
- ID: 242588
Cite item
Abstract
The inverse dynamic problem for the wave equation with a potential on a real line is considered. The forward initial-boundary value problem is set up with the help of boundary triplets. As an inverse data, an analog of the response operator (dynamic Dirichlet-to-Neumann map) is used. Equations of the inverse problem are derived; also, a relationship between the dynamic inverse problem and the spectral inverse problem from a matrix-valued measure is pointed out.
About the authors
A. S. Mikhaylov
St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg State University
Author for correspondence.
Email: mikhaylov@pdmi.ras.ru
Russian Federation, St.Petersburg
V. S. Mikhaylov
St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg State University
Email: mikhaylov@pdmi.ras.ru
Russian Federation, St.Petersburg