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

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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.

About the authors

Alexander M. Romanenkov

Moscow Aviation Institute (National Research University); Federal Research Center “Computer Science and Control” of Russian Academy of Sciences

Author for correspondence.
Email: romanaleks@gmail.com
ORCID iD: 0000-0002-0700-8465
SPIN-code: 7586-0934
Scopus Author ID: 57196480014
ResearcherId: AAH-9530-2020
https://www.mathnet.ru/rus/person29785

Cand. Techn. Sci., Associate Professor; Associate Professor; Dept. of Mathematics; Senior Researcher; Dept. of Mathematical Modeling of Heterogeneous Systems

Russian Federation, 125993, Moscow, Volokolamskoe Shosse, 4; 119333, Moscow, Vavilova str., 44/2

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