This article is cited in 1 paper

Control processes

On the boundary control problem for a pseudo-parabolic equation with involution

F. N. Dekhkonov

Namangan State University, 316, ul. Uychi, Namangan, 160136, Uzbekistan

Abstract: Previously, some control problems for the pseudo-parabolic equation independent of involution were considered. In this paper, we consider a boundary control problem associated with a pseudo-parabolic equation with involution in a bounded one-dimensional domain. On the part of the border of the considered domain, the value of the solution with control function is given. Restrictions on the control are given in such a way that the average value of the solution in the considered domain gets a given value. The problem given by the method of separation of variables is reduced to the Volterra integral equation of the second kind. The existence of the control function was proved by the Laplace transform method.

Keywords: boundary problem, Volterra integral equation, control function, Laplace transform, involution.

UDC: 517.977

MSC: 35K70

Received: March 9, 2024
Accepted: June 25, 2024

Language: English

DOI: 10.21638/spbu10.2024.309