A. S. Mikhaylov, V. S. Mikhaylov, A. E. Choque-Rivero, “Dynamic inverse problem for the one-dimensional system with memory”, Zap. Nauchn. Sem. POMI, 2020, Volume 493,Pages <nobr>259

Dynamic inverse problem for the one-dimensional system with memory

A. S. Mikhaylov^a, V. S. Mikhaylov^b, A. E. Choque-Rivero^c

^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

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.

UDC: 517

Received: 05.11.2020