Initial Problem for Two-Dimensional Hyperbolic Equation with a Nonlocal Term

Vladimir Vasilyev () and Natalya Zaitseva
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Vladimir Vasilyev: Center of Applied Mathematics, Belgorod State National Research University, Pobedy Street 85, Belgorod 308015, Russia
Natalya Zaitseva: Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow 119991, Russia

Mathematics, 2022, vol. 11, issue 1, 1-24

Abstract: In this paper, we study the Cauchy problem in a strip for a two-dimensional hyperbolic equation containing the sum of a differential operator and a shift operator acting on a spatial variable that varies over the real axis. An operating scheme is used to construct the solutions of the equation. The solution of the problem is obtained in the form of a convolution of the function found using the operating scheme and the function from the initial conditions of the problem. It is proved that classical solutions of the considered initial problem exist if the real part of the symbol of the differential-difference operator in the equation is positive.

Keywords: hyperbolic equation; differential-difference equation; initial problem; Fourier transform; operational scheme (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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