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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Vladimir Vasilyev & Natalya Zaitseva, 2022. "Initial Problem for Two-Dimensional Hyperbolic Equation with a Nonlocal Term," Mathematics, MDPI, vol. 11(1), pages 1-24, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:130-:d:1016884
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