Short Communication
Differential Equations and Mathematical Physics

On the uniqueness of solutions to initial-boundary value problems for high-order linear pseudohyperbolic equations

A. M. Romanenkov<sup>ab

a</sup> Moscow Aviation Institute (National Research University), Moscow, 125993, Russian Federation
^b Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, Moscow, 119333, Russian Federation

Abstract: This study investigates the uniqueness of solutions to initial-boundary value problems representing a generalized mathematical model of oscillations in elastic structures (strings, rods, and various types of beams). These processes are described by hyperbolic and pseudohyperbolic-type partial differential equations of order higher than second (fourth, sixth, etc.). Specific model equations of oscillations are examined in detail. For the general initial-boundary value problem of a linear differential oscillation equation with variable coefficients depending solely on the spatial variable, an energy identity satisfied by the solutions is derived using integral estimates. Furthermore, a uniqueness theorem for the solution is established.

Keywords: high-order pseudohyperbolic equation, energy identity, solution uniqueness

UDC: 517.956.32

MSC: 35L76, 35B30, 35G15

Received: February 25, 2025
Revised: June 27, 2025
Accepted: July 8, 2025
First online: August 13, 2025

DOI: 10.14498/vsgtu2161

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