Mathematical Modelling

On the mathematical model of the control problem for a pseudo-parabolic equation with involution

F. N. Dekhkonov

Namangan State University, Namangan, Uzbekistan

Abstract: In this paper, we consider the mathematical model of control problem for a pseudo-parabolic equation with involution in a bounded two-dimensional domain. The solution with the control function on the border of the considered domain is given. The constraints on the control are determined to ensure that the average value of the solution within the considered domain attains a given value. The initial-boundary problem is solved by the Fourier method, and the control problem under consideration is analyzed with the Volterra integral equation of the second kind. The existence of admissible control is proved by the Laplace transform method.

Keywords: pseudo-parabolic equation, mathematical model, boundary problem, Volterra integral equation, admissible control, Laplace transform, involution.

MSC: 35K70

Received: 18.08.2024

Language: English

DOI: 10.14529/mmp250201