najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2025-16-5-563-576najo-1527Research ArticleMATHEMATICSМАТЕМАТИКАNonlinear optimal control problem in a two-point boundary regime for a pseudoparabolic equation with Samarskii–Ionkin type conditionsНелинейное оптимальное управление в двухточечной краевой задаче для псевдопараболического уравнения с условиями типа Самарского-Ионкинаhttps://orcid.org/0000-0002-9346-5362ЮлдашевТ. К.YuldashevT. K.

Tursun K. Yuldashev

Temiryolchilar 1, Tashkent, 100174; Lenin Avenue, 331, Osh 723500

tursun.k.yuldashev@gmail.comhttps://orcid.org/0000-0001-8937-0523КадиркуловБ. Ж.KadirkulovB. J.

Bakhtiyar J. Kadirkulov

Tashkent

bb.kadirkulov@afu.uzhttps://orcid.org/0000-0003-0166-6018РамазановаА. Т.RamazanovaA. T.

Aysel T. Ramazanova

Essen

ramazanovaaysel897@gmail.comhttps://orcid.org/0009-0002-1325-0044ШермаматовЖ. Ж.ShermamatovZh. Zh.

Zholdoshbek Zh. Shermamatov

Lenin Avenue, 331, Osh 723500

jshermamatov@oshsu.kgTashkent State Transport University; Osh State UniversityUzbekistanAlfraganus UniversityUzbekistanUniversitat Duisburg-EssenGermanyOsh State UniversityKyrgyzstan202505112025165563576Copyright © Yuldashev T.K., Kadirkulov B.J., Ramazanova A.T., Shermamatov Z.Z., 20252025Юлдашев Т.К., Кадиркулов Б.Ж., Рамазанова А.Т., Шермаматов Ж.Ж.Yuldashev T.K., Kadirkulov B.J., Ramazanova A.T., Shermamatov Z.Z.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1527

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.

В данной работе рассматривается задача оптимального управления подвижной точкой для псевдопараболического уравнения с нелинейной управляющей функцией при двухточечном нелинейном граничном условии. Уравнение исследуется при краевых условиях типа Самарского-Ионкина по пространственной переменной x. Изучена спектральная задача и найдены собственные значения, собственные функции и условия оптимальности. Получены нагруженные нелинейные функциональные уравнения относительно управляющей функции. Методом сжимающих отображений доказано существование и единственность управляющей функции. Определена функция состояния. Доказана сходимость ряда Фурье для функции состояния.

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The authors declare that there are no conflicts of interest present.