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A Classical Solution to a Hyperbolic Differential-Difference Equation with a Translation by an Arbitrary Vector

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Abstract

Using an operational scheme, a three-parameter family of solutions is constructed in a half-space for a multidimensional hyperbolic differential-difference equation with translation operators of the general type acting on all spatial variables. The theorem is proved stating that the obtained solutions are classical, provided that the real part of the symbol of the differential-difference operator is positive. Classes of equations are given for which the indicated condition is satisfied.

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Funding

This study was carried out by the first author with financial support from the Ministry of Science and Higher Education of Russia as part of the program for the Moscow Center of Fundamental and Applied Mathematics, agreement no. 075-15-2022-284. The contribution of the second author was made with financial support from the Ministry of Science and Higher Education of Russia as part of State Task project no. FSSF-2023-0016.

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Authors and Affiliations

  1. Lomonosov Moscow State University, 119991, Moscow, Russia

    N. V. Zaitseva

  2. Peoples’ Friendship University of Russia, 117198, Moscow, Russia

    A. B. Muravnik

Authors
  1. N. V. Zaitseva
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  2. A. B. Muravnik
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Corresponding authors

Correspondence to N. V. Zaitseva or A. B. Muravnik.

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The authors declare that they have no conflicts of interest.

Additional information

Translated by A.V. Shishulin

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Zaitseva, N.V., Muravnik, A.B. A Classical Solution to a Hyperbolic Differential-Difference Equation with a Translation by an Arbitrary Vector. Russ Math. 67, 29–34 (2023). https://doi.org/10.3103/S1066369X23050110

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  • DOI: https://doi.org/10.3103/S1066369X23050110

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