On Hyperbolic Equations with a Translation Operator in Lowest Derivatives

Vladimir Vasilyev () and Natalya Zaitseva
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Vladimir Vasilyev: Center of Applied Mathematics, Belgorod State National Research University, Pobedy St. 85, Belgorod 308015, Russia
Natalya Zaitseva: Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow 119991, Russia

Mathematics, 2024, vol. 12, issue 12, 1-8

Abstract: In the half-plane, a solution to a two-dimensional hyperbolic equation with a translation operator in the lowest derivative with respect to a spatial variable varying along the entire real axis is constructed in an explicit form. It is proven that the solutions obtained are classical if the real part of the symbol of a differential-difference operator in the equation is positive.

Keywords: hyperbolic equation; differential-difference equation; translation operator; classical solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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