Nonlinear optimal control problem in a two-point boundary regime for a pseudoparabolic equation with Samarskii–Ionkin type conditions
https://doi.org/10.17586/2220-8054-2025-16-5-563-576
Abstract
This paper is devoted to study a optimal movable point control problem for a pseudoparabolic equation with nonlinear control function in a two-point nonlinear boundary condition. The equation is studied with Samarskii–Ionkin type boundary conditions on spatial variable x. Spectral problem is studied and eigenvalues, eigenfunctions and optimality conditions are found. Loaded nonlinear functional equations are obtained with respect to control function. We prove the existence and uniqueness of the control function by the method of compressing mapping. The state function is determined. Convergence of the Fourier series for the state function is proved.
About the Authors
T. K. Yuldashev
Tashkent State Transport University; Osh State University
Uzbekistan
Uzbekistan
Tursun K. Yuldashev
Temiryolchilar 1, Tashkent, 100174; Lenin Avenue, 331, Osh 723500
B. J. Kadirkulov
Alfraganus University
Uzbekistan
Uzbekistan
Bakhtiyar J. Kadirkulov
Tashkent
A. T. Ramazanova
Universitat Duisburg-Essen
Germany
Germany
Aysel T. Ramazanova
Essen
Zh. Zh. Shermamatov
Osh State University
Kyrgyzstan
Kyrgyzstan
Zholdoshbek Zh. Shermamatov
Lenin Avenue, 331, Osh 723500
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Yuldashev T.K., Kadirkulov B.J., Ramazanova A.T., Shermamatov Zh.Zh. Nonlinear optimal control problem in a two-point boundary regime for a pseudoparabolic equation with Samarskii–Ionkin type conditions. Nanosystems: Physics, Chemistry, Mathematics. 2025;16(5):563-576. https://doi.org/10.17586/2220-8054-2025-16-5-563-576
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