ON THE ENERGY INTEGRALS OF A MIXED PROBLEM FOR A B-HYPERBOLIC EQUATION

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.