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Sibirsk. Mat. Zh., 2025 Volume 66, Number 6, Pages 1063–1073 (Mi smj7998)

On a class of pseudohyperbolic operators with variable coefficients

G. V. Demidenkoab, X. Maab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: We consider a class of strictly pseudohyperbolic operators of the sixth order with variable coefficients. The class contains, in particular, the generalized Boussinesq operator. Under certain conditions on the coefficients, energy estimates are established.

Keywords: equations not resolved with respect to the highest derivative, pseudohyperbolic operators, energy estimates, weighted Sobolev spaces.

UDC: 517.955

MSC: 35R30

Received: 01.08.2025
Revised: 01.08.2025
Accepted: 27.08.2025

DOI: 10.33048/smzh.2025.66.606


 English version:
Siberian Mathematical Journal, 2025, 66:6, 1395–1404


© Steklov Math. Inst. of RAS, 2026