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

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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

About the authors

Farrukh N. Dekhkonov

Namangan State University

Author for correspondence.
Email: f.n.dehqonov@mail.ru
ORCID iD: 0000-0003-4747-8557

Candidate of Physics and Mathematics, Associate Professor of the Mathematical Analysis Department

Uzbekistan, 316 Uychi St., Namangan 1600136, Uzbekistan

Batirkhan Kh. Turmetov

Khoja Akhmet Yassawi International Kazakh-Turkish University; Alfraganus University

Email: batirkhan.turmetov@ayu.edu.kz
ORCID iD: 0000-0001-7735-6484

Doctor of Physics and Mathematics, Professor, Department of Mathematics; Professor, Department of Mathematics and Physics

Uzbekistan, 29 Bekzat Sattarhanov St., Turkistan 161200, Kazakhstan; 2a Yukori Karakamish Str., Tashkent 100190, Uzbekistan

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