Inverse dynamic problem for the wave equation with periodic boundary conditions
https://doi.org/10.17586/2220-8054-2019-10-2-115-123
Abstract
We consider the inverse dynamic problem for the wave equation with a potential on an interval (0; 2π) with periodic boundary conditions. We use a boundary triplet to set up the initial-boundary value problem. As inverse data we use a response operator (dynamic Dirichlet-to-Neumann map). Using the auxiliary problem on the whole line, we derive equations of the inverse problem. We also establish the relationships between dynamic and spectral inverse data.
Supporting agencies: The research of Victor Mikhaylov was supported by RFBR 17-01-00529. Alexandr Mikhaylov was supported by RFBR 17-01-00099; A. S. Mikhaylov and V. S. Mikhaylov were partly supported by RFBR 18-01-00269 and by the Ministry of Education and Science of Republic of Kazakhstan under grant AP05136197.
About the Authors
A. S. Mikhaylov
Saint Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences ; Saint Petersburg State University
Russian Federation
Russian Federation
7, Fontanka, Saint Petersburg, 191023
7/9 Universitetskaya nab., Saint Petersburg, 199034
V. S. Mikhaylov
Saint Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences ; Saint Petersburg State University
Russian Federation
Russian Federation
7, Fontanka, Saint Petersburg, 191023
7/9 Universitetskaya nab., Saint Petersburg, 199034
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For citations:
Mikhaylov A.S., Mikhaylov V.S. Inverse dynamic problem for the wave equation with periodic boundary conditions. Nanosystems: Physics, Chemistry, Mathematics. 2019;10(2):115-123. https://doi.org/10.17586/2220-8054-2019-10-2-115-123
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