C&SA | Contents

Volume 61 >>> № 1 JANUARY — FEBRUARY 2025

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DOI 10.34229/KCA2522-9664.25.1.8

UDC 517.977.5

A.V. Anikushyn¹, Kh.M. Hranishak²,
V.S. Lyashko³, O.S. Samosonok⁴

¹ Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

andrii.anikushyn@knu.ua

² Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

kristinka.granishak@gmail.com

³ V.M. Glushkov Institute of Cybernetics,
National Academy of Sciences of Ukraine,
Kyiv, Ukraine

lyashko91@gmail.com

⁴ V.M. Glushkov Institute of Cybernetics,
National Academy of Sciences of Ukraine,
Kyiv, Ukraine

samosyonok@gmail.com

OPTIMAL CONTROL OF HYPERBOLIC INTEGRO-DIFFERENTIAL SYSTEMS

Abstract. We prove a priori inequalities for the class of linear integro-differential equations of hyperbolic type that arise in the analysis of viscoelastic media. Theorems of the existence and uniqueness of the generalized solution and the continuous dependence of the solution on the equation’s right-hand side are formulated. The problem of optimal control is given, and a theorem on the existence of its solution is formulated.

Keywords: a priori estimates, generalized solvability, optimal control, integro-differential equation, hyperbolic equation.

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