Mathematics

Energy estimates for an uniformly strictly pseudohyperbolic operator

G. V. Demidenko^ab, V. S. Nurmakhmatov<sup>b

a</sup> Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: A class of strictly pseudohyperbolic operators of the fourth order with variable coefficients is considered. This class includes, in particular, the Vlasov, Gal'pern, and Rayleigh–Bishop operators. Under certain conditions for the coefficients, energy estimates are established.

Keywords: equation not solvable with respect to the highest-order derivative, pseudohyperbolic operator, energy estimate, weighted Sobolev space.

UDC: 517.955

Received: 12.09.2025
Revised: 06.10.2025

DOI: 10.47475/2500-0101-2025-10-4-649-663