NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2019, 10 (2), P. 115–123
Inverse dynamic problem for the wave equation with periodic boundary conditions
A. S. Mikhaylov – Saint Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, 7, Fontanka, Saint Petersburg, 191023; Saint Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg, 199034 Russia; mikhaylov@pdmi.ras.ru
V. S. Mikhaylov – Saint Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, 7, Fontanka, Saint Petersburg, 191023; Saint Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg, 199034 Russia; vsmikhaylov@pdmi.ras.ru
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.
Keywords: inverse problem, Boundary Control method, Schrödinger operator.
DOI 10.17586/2220-8054-2019-10-2-115-123