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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2023, Number 5, Pages 34–40
DOI: https://doi.org/10.26907/0021-3446-2023-5-34-40 (Mi ivm9876) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Classical solutions of hyperbolic differential-difference equation with shift by an arbitrary vector

N. V. Zaitsevaa, A. B. Muravnikb

a Lomonosov Moscow State University, Moscow Center for Fundamental and Applied Mathematics, GSP-1, 1 Leninskie Gory, Moscow, 119991 Russia
b Peoples Friendship University of Russia, 6 Miklukho--Maklaya str., Moscow, 117198 Russia
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DOI: https://doi.org/10.26907/0021-3446-2023-5-34-40
Abstract: We construct three-parameter family of solutions in a half-space for the multidimensional hyperbolic differential-difference equation with shift operators of the general type acting on all spatial variables. Solutions are built using an operating scheme. We prove the theorem stating that these solutions are classical under the condition that the real part of the symbol of the differential-difference operator is positive. Classes of equations for which the indicated condition is satisfied are given.
Keywords: hyperbolic equation, differential-difference equation, classical solution, Fourier transform.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-284
FSSF-2023-0016
Received: 16.08.2022
Revised: 27.09.2022
Accepted: 21.12.2022
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2023, Volume 67, Issue 5, Pages 29–34
DOI: https://doi.org/10.3103/S1066369X23050110
Document Type: Article
UDC: 517.956.32: 517.929
Language: Russian
Citation: N. V. Zaitseva, A. B. Muravnik, “Classical solutions of hyperbolic differential-difference equation with shift by an arbitrary vector”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 5, 34–40; Russian Math. (Iz. VUZ), 67:5 (2023), 29–34
Citation in format AMSBIB
\Bibitem{ZaiMur23}
\by N.~V.~Zaitseva, A.~B.~Muravnik
\paper Classical solutions of hyperbolic differential-difference equation with shift by an arbitrary vector
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2023
\issue 5
\pages 34--40
\mathnet{http://mi.mathnet.ru/ivm9876}
\crossref{https://doi.org/10.26907/0021-3446-2023-5-34-40}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2023
\vol 67
\issue 5
\pages 29--34
\crossref{https://doi.org/10.3103/S1066369X23050110}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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