Geodesic
Dynamic inverse problem for the one-dimensional system with memory
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 50, Tome 493 (2020), pp. 259-268

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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. 
@article{ZNSL_2020_493_a16,
     author = {A. S. Mikhaylov and V. S. Mikhaylov and A. E. Choque-Rivero},
     title = {Dynamic inverse problem for the one-dimensional system with memory},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {259--268},
     publisher = {mathdoc},
     volume = {493},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a16/}
}
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A. S. Mikhaylov; V. S. Mikhaylov; A. E. Choque-Rivero. Dynamic inverse problem for the one-dimensional system with memory. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 50, Tome 493 (2020), pp. 259-268. http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a16/