najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2019-10-2-115-123najo-625Research ArticleMATHEMATICSМАТЕМАТИКАInverse dynamic problem for the wave equation with periodic boundary conditionsMikhaylovA. S.

7, Fontanka, Saint Petersburg, 191023  

7/9 Universitetskaya nab., Saint Petersburg, 199034 

mikhaylov@pdmi.ras.ruMikhaylovV. S.

7, Fontanka, Saint Petersburg, 191023  

7/9 Universitetskaya nab., Saint Petersburg, 199034 

vsmikhaylov@pdmi.ras.ruSaint Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences ; Saint Petersburg State UniversityRussian Federation201912082025102115123Copyright © Mikhaylov A.S., Mikhaylov V.S., 20252025Mikhaylov A.S., Mikhaylov V.S.Mikhaylov A.S., Mikhaylov V.S.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/625

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.

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The authors declare that there are no conflicts of interest present.