Classical Solutions of Hyperbolic Equation with Translation Operators in Free Terms

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, 2023, vol. 11, issue 14, 1-9

Abstract: In this paper, we study the question of constructing explicit solutions in a half-space of a hyperbolic equation containing translation operators in space variables in all coordinate directions. Such equations are a natural generalization of classical equations of hyperbolic type, and the resulting solution relates the value of the desired function at different points of the half-space where the process takes place. To construct solutions, a classical operating scheme is used, namely, the formal application of an integral transformation. A theorem is proved that the constructed solutions are classical if the real part of the symbol of the differential-difference operator in the equation is positive. Classes of equations for which this condition is satisfied are given.

Keywords: hyperbolic equation; differential-difference equation; translation operator; classical solution; operational scheme (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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