Optimal Control Problems for Evolutionary Variational Inequalities with Volterra-Type Operators

Optimal Control Problems for Evolutionary Variational Inequalities with Volterra-Type Operators

In this paper, we consider an optimal control problem for a class of evolution inclusions with Volterra-type operators. The existence and uniqueness results for the initial value problem for such inclusions were obtained in our previous work. Here we establish the existence of a solution to the stat...

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Date:2024
Main Authors: Bokalo, Mykola, Sus, Olha
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2024
Subjects:
параболiчна варiацiйна нерiвнiсть
еволюцiйна варiацiйна нерiвнiсть
оператор типу Вольтерра
оптимальне керування
Online Access:https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1051
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Journal Title:Journal of Mathematical Physics, Analysis, Geometry

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Journal of Mathematical Physics, Analysis, Geometry
id oai:jmag.ilt.kharkiv.ua:article-1051
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spelling oai:jmag.ilt.kharkiv.ua:article-10512024-12-10T20:10:54Z Optimal Control Problems for Evolutionary Variational Inequalities with Volterra-Type Operators Optimal Control Problems for Evolutionary Variational Inequalities with Volterra-Type Operators Optimal Control Problems for Evolutionary Variational Inequalities with Volterra-Type Operators Bokalo, Mykola Sus, Olha параболiчна варiацiйна нерiвнiсть еволюцiйна варiацiйна нерiвнiсть оператор типу Вольтерра оптимальне керування parabolic variational inequality evolutionary variational inequality Volterra-type operator optimal control In this paper, we consider an optimal control problem for a class of evolution inclusions with Volterra-type operators. The existence and uniqueness results for the initial value problem for such inclusions were obtained in our previous work. Here we establish the existence of a solution to the stated optimal control problem under some hypothesis on data-in. The motivation for this work comes from the optimal control problems for variational inequalities arising in the study of injection molding processes, contact mechanics, processes of electro-wetting on dielectrics, and others. Mathematical Subject Classification 2020: 34H05, 35K86, 49J20, 49J21,49J27, 49J40 У цiй статтi розглядаємо задачу оптимального керування для класу еволюцiйних субдиференцiальних включень з операторами типу Вольтерра. Результати стосовно iснування та єдиностi розв’язку задачi з початковою умовою для таких включень були отриманi в попереднiй нашiй роботi. Тут встановлюємо iснування розв’язку поставленої задачi оптимального керування за деяких припущень на вхiднi данi. Мотивацiєю для цiєї роботи є задачi оптимального керування системами, що описуються еволюцiйними варiацiйними нерiвностями, що виникають при вивченнi процесiв лиття пiд тиском, контактної механiки, процесiв електрозмочування дiелектрика та iнших. Mathematical Subject Classification 2020: 34H05, 35K86, 49J20, 49J21,49J27, 49J40 Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2024-04-01 Article Article application/pdf https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1051 10.15407/mag20.01.025 Journal of Mathematical Physics, Analysis, Geometry; Vol. 20 No. 1 (2024); 25–40 Журнал математической физики, анализа, геометрии; Том 20 № 1 (2024); 25–40 Журнал математичної фізики, аналізу, геометрії; Том 20 № 1 (2024); 25–40 1817-5805 1812-9471 en https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1051/jm20-0025e
institution Journal of Mathematical Physics, Analysis, Geometry
baseUrl_str
datestamp_date 2024-12-10T20:10:54Z
collection OJS
language English
topic параболiчна варiацiйна нерiвнiсть
еволюцiйна варiацiйна нерiвнiсть
оператор типу Вольтерра
оптимальне керування
spellingShingle параболiчна варiацiйна нерiвнiсть
еволюцiйна варiацiйна нерiвнiсть
оператор типу Вольтерра
оптимальне керування
Bokalo, Mykola
Sus, Olha
Optimal Control Problems for Evolutionary Variational Inequalities with Volterra-Type Operators
topic_facet параболiчна варiацiйна нерiвнiсть
еволюцiйна варiацiйна нерiвнiсть
оператор типу Вольтерра
оптимальне керування
parabolic variational inequality
evolutionary variational inequality
Volterra-type operator
optimal control
format Article
author Bokalo, Mykola
Sus, Olha
author_facet Bokalo, Mykola
Sus, Olha
author_sort Bokalo, Mykola
title Optimal Control Problems for Evolutionary Variational Inequalities with Volterra-Type Operators
title_short Optimal Control Problems for Evolutionary Variational Inequalities with Volterra-Type Operators
title_full Optimal Control Problems for Evolutionary Variational Inequalities with Volterra-Type Operators
title_fullStr Optimal Control Problems for Evolutionary Variational Inequalities with Volterra-Type Operators
title_full_unstemmed Optimal Control Problems for Evolutionary Variational Inequalities with Volterra-Type Operators
title_sort optimal control problems for evolutionary variational inequalities with volterra-type operators
title_alt Optimal Control Problems for Evolutionary Variational Inequalities with Volterra-Type Operators
Optimal Control Problems for Evolutionary Variational Inequalities with Volterra-Type Operators
description In this paper, we consider an optimal control problem for a class of evolution inclusions with Volterra-type operators. The existence and uniqueness results for the initial value problem for such inclusions were obtained in our previous work. Here we establish the existence of a solution to the stated optimal control problem under some hypothesis on data-in. The motivation for this work comes from the optimal control problems for variational inequalities arising in the study of injection molding processes, contact mechanics, processes of electro-wetting on dielectrics, and others. Mathematical Subject Classification 2020: 34H05, 35K86, 49J20, 49J21,49J27, 49J40
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
publishDate 2024
url https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1051
work_keys_str_mv AT bokalomykola optimalcontrolproblemsforevolutionaryvariationalinequalitieswithvolterratypeoperators
AT susolha optimalcontrolproblemsforevolutionaryvariationalinequalitieswithvolterratypeoperators
first_indexed 2025-09-26T01:40:41Z
last_indexed 2025-09-26T01:40:41Z
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