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

О задаче управления для псевдопараболического уравнения с инволюцией в ограниченной области
Dekhkonov F.N. Turmetov B.Kh.
2025 Tambov State University

Vestnik Rossiyskikh Universitetov. Matematika
2025 #30 Issue 152 322 - 337 pp.

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.

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

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Mathematical Analysis Department, Namangan State University, 316 Uychi St., Namangan, 1600136, Uzbekistan
Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, 29 Bekzat Sattarhanov St., Turkistan, 161200, Kazakhstan
Department of Mathematics and Physics, Alfraganus University, 2a Yukori Karakamish Str., Tashkent, 100190, Uzbekistan

Mathematical Analysis Department
Department of Mathematics
Department of Mathematics and Physics

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