Geodesic
Inverse dynamic problem for the wave equation with periodic boundary conditions
Nanosistemy: fizika, himiâ, matematika, Tome 10 (2019) no. 2, pp. 115-123.

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We consider the inverse dynamic problem for the wave equation with a potential on an interval $(0 , 2\pi)$ 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. 
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     author = {A. S. Mikhailov and V. S. Mikhailov},
     title = {Inverse dynamic problem for the wave equation with periodic boundary conditions},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {115--123},
     publisher = {mathdoc},
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     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2019_10_2_a0/}
}
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A. S. Mikhailov; V. S. Mikhailov. Inverse dynamic problem for the wave equation with periodic boundary conditions. Nanosistemy: fizika, himiâ, matematika, Tome 10 (2019) no. 2, pp. 115-123. http://geodesic.mathdoc.fr/item/NANO_2019_10_2_a0/