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Matematicheskie Zametki, 2022, Volume 112, Issue 6, Pages 810–819
DOI: https://doi.org/10.4213/mzm13524 (Mi mzm13524) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Classical Solutions of a Multidimensional Hyperbolic Differential–Difference Equation with Shifts of Various Directions in the Potentials

N. V. Zaitsevaab

a Lomonosov Moscow State University
b Moscow Center for Fundamental and Applied Mathematics
Full-text PDF (450 kB) Citations (9)
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DOI: https://doi.org/10.4213/mzm13524
Abstract: We study the existence of smooth solutions of a multidimensional hyperbolic equation containing the sum of differential operators and shift operators along arbitrary spatial coordinate directions. For this equation, we construct a three-parameter family of solutions. It is proved that the resulting solutions are classical under the condition that the real part of the symbol of the differential–difference operator in the equation is positive. Classes of equations for which this condition holds are given.
Keywords: hyperbolic equation, differential–difference equation, classical solution, operational scheme, Fourier transform.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-284
This work was supported by the Ministry of Science and Higher Education of the Russian Federation within the framework of the program of the Moscow Center for Fundamental and Applied Mathematics under agreement no. 075-15-2022-284.
Received: 02.04.2022
Published: 04.12.2022
English version:
Mathematical Notes, 2022, Volume 112, Issue 6, Pages 872–880
DOI: https://doi.org/10.1134/S0001434622110219
Bibliographic databases:
Document Type: Article
UDC: 517.956.32+517.929
Language: Russian
Citation: N. V. Zaitseva, “Classical Solutions of a Multidimensional Hyperbolic Differential–Difference Equation with Shifts of Various Directions in the Potentials”, Mat. Zametki, 112:6 (2022), 810–819; Math. Notes, 112:6 (2022), 872–880
Citation in format AMSBIB
\Bibitem{Zai22}
\by N.~V.~Zaitseva
\paper Classical Solutions of a Multidimensional Hyperbolic Differential--Difference Equation with Shifts of Various Directions in the Potentials
\jour Mat. Zametki
\yr 2022
\vol 112
\issue 6
\pages 810--819
\mathnet{http://mi.mathnet.ru/mzm13524}
\crossref{https://doi.org/10.4213/mzm13524}
\transl
\jour Math. Notes
\yr 2022
\vol 112
\issue 6
\pages 872--880
\crossref{https://doi.org/10.1134/S0001434622110219}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85145383723}
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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