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.
@article{NANO_2019_10_2_a0,
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},
volume = {10},
number = {2},
year = {2019},
language = {en},
url = {http://geodesic.mathdoc.fr/item/NANO_2019_10_2_a0/}
}
TY - JOUR AU - A. S. Mikhailov AU - V. S. Mikhailov TI - Inverse dynamic problem for the wave equation with periodic boundary conditions JO - Nanosistemy: fizika, himiâ, matematika PY - 2019 SP - 115 EP - 123 VL - 10 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/NANO_2019_10_2_a0/ LA - en ID - NANO_2019_10_2_a0 ER -
%0 Journal Article %A A. S. Mikhailov %A V. S. Mikhailov %T Inverse dynamic problem for the wave equation with periodic boundary conditions %J Nanosistemy: fizika, himiâ, matematika %D 2019 %P 115-123 %V 10 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/NANO_2019_10_2_a0/ %G en %F NANO_2019_10_2_a0
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/