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On Global Classical Solutions of Hyperbolic Differential-Difference Equations

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Abstract

A one-parameter family of global solutions of a two-dimensional hyperbolic differential-difference equation with an operator acting with respect to a space variable is constructed. A theorem is proved stating that the resulting solutions are classical for all parameter values if the symbol of the difference operator of the equation has a positive real part. Classes of equations for which this condition is satisfied are given.

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ACKNOWLEDGMENTS

The author is deeply grateful to I.S. Lomov for giving valuable advice, to A.B. Muravnik for suggesting the problem and helpful comments, and to A.L. Skubachevskii for taking an interest in this work.

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Authors and Affiliations

  1. Kazan (Volga Region) Federal University, Kazan, Russia

    N. V. Zaitseva

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  1. N. V. Zaitseva
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Correspondence to N. V. Zaitseva.

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Translated by I. Ruzanova

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Zaitseva, N.V. On Global Classical Solutions of Hyperbolic Differential-Difference Equations. Dokl. Math. 101, 115–116 (2020). https://doi.org/10.1134/S1064562420020246

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  • DOI: https://doi.org/10.1134/S1064562420020246

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