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

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.