Scientific articles

On the control problem for a pseudo-parabolic equation with involution in a bounded domain

F. N. Dekhkonov^a, B. Kh. Turmetov<sup>bc

a</sup> Namangan State University
^b Alfraganus University
^c Khoja Akhmet Yassawi International Kazakh-Turkish University

Abstract: This paper considers a control problem for a pseudo-parabolic equation with an involution operator in a bounded domain. A generalized solution to the corresponding initial boundary value problem is obtained. By introducing an additional integral condition, the control problem is reduced to a Volterra integral equation of the first kind. To show that the integral equation has a solution, some estimates are obtained for the kernel of this integral equation. The existence of a solution to the integral equation is shown using the Laplace transform method and the admissibility of the control function is proved.

Keywords: pseudo-parabolic equation, Volterra integral equation, admissible control, initial boundary value problem, Laplace transform, weight function

UDC: 517.977

MSC: 35K70, 35K35

Received: 02.05.2025
Accepted: 21.11.2025

Language: English

DOI: 10.20310/2686-9667-2025-30-152-322-337