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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2022 Volume 208, Pages 29–36 (Mi into992)

Asymptotic problem of restoring the high-frequency right-hand side of the telegraph equation

E. V. Korablinaab, V. B. Levenshtamba

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Southern Federal University, Rostov-on-Don

Abstract: In this paper, we consider the Cauchy problem for the telegraph equation. The lower coefficient and the right-hand side of the equation oscillate in time with a high frequency, the amplitude of the lower coefficient is small, namely, is inversely proportional to the frequency, and the right-hand side is unknown. We examine the problem on the recovery of the right-hand side from the three-term asymptotics of the solution given at some point in space. For this purpose, we use a nonclassical algorithm for solving inverse coefficient problems with rapidly oscillating data.

Keywords: inverse problem, asymptotic methods, telegraph equation, rapidly oscillating data.

UDC: 517.928

MSC: 34D05

DOI: 10.36535/0233-6723-2022-208-29-36



© Steklov Math. Inst. of RAS, 2025