MATHEMATICS

On the energy integrals of a mixed problem for a B-hyperbolic equation

L. N. Lyakhov<sup>abc

a</sup> Voronezh State University, Voronezh, Russia
^b Lipetsk State Pedagogical University named after P.P. Semenov-Tyan-Shan, Lipetsk, Russia
^c I. A. Bunin Elets State University, Yelets, Russia

Abstract: A mixed problem for the B-hyperbolic equation in Euclidean domains with different locations relative to singular coordinate hyperplanes is considered. In each of these domains, energy integrals with respect to the Lebesgue–Kipriyanov integral measure with weak and strong singularities are introduced. The absence of energy flow through coordinate singular hyperplanes, which are the internal boundary of mirror-symmetric regions in Euclidean space, is proven. If solutions to these problems exist, their uniqueness is proven.

Keywords: Laplace–Bessel operator, B-hyperbolic equation, mixed problem, energy integral, energy flow, uniqueness.

UDC: 519.6

Presented: I. A. Sokolov
Received: 31.03.2025
Revised: 06.06.2025
Accepted: 11.06.2025

DOI: 10.31857/S2686954325030109

 English version: Doklady Mathematics, 2025, 111:3, 189–194

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