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Zapiski Nauchnykh Seminarov POMI, 2020, Volume 493, Pages 259–268 (Mi znsl6970)  
Dynamic inverse problem for the one-dimensional system with memory

A. S. Mikhaylova, V. S. Mikhaylovb, A. E. Choque-Riveroc

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Saint Petersburg State University
c Universidad Michoacana de San Nicolás de Hidalgo
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Abstract: We study the inverse dynamic problem of recoverying the potential in the one-dimensional dynamical system with memory. The Gelfand–Levitan equations are derived for the kernel of the integral operator which is inverse to the control operator of the system. The potential is reconstructed from the solution of these equations.
Key words and phrases: equations with memory, inverse problem, Gelfand–Levitan equations, Boundary control method.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00269_а
20-01-00627
Volkswagen Foundation
CONACYT - Consejo Nacional de Ciencia y Tecnología A1-S-31524
Coordinacion de la Investigacion Cientifica, Universidad Michoacana de San Nicolas de Hidalgo
Received: 05.11.2020
Document Type: Article
UDC: 517
Language: Russian
Citation: A. S. Mikhaylov, V. S. Mikhaylov, A. E. Choque-Rivero, “Dynamic inverse problem for the one-dimensional system with memory”, Mathematical problems in the theory of wave propagation. Part 50, Zap. Nauchn. Sem. POMI, 493, POMI, St. Petersburg, 2020, 259–268
Citation in format AMSBIB
\Bibitem{MikMikCho20}
\by A.~S.~Mikhaylov, V.~S.~Mikhaylov, A.~E.~Choque-Rivero
\paper Dynamic inverse problem for the one-dimensional system with memory
\inbook Mathematical problems in the theory of wave propagation. Part~50
\serial Zap. Nauchn. Sem. POMI
\yr 2020
\vol 493
\pages 259--268
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6970}
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