On the boundary control problem for  a pseudo-parabolic equation with involution:

Фаррух Нуриддинович  Дехконов

doi:10.21638/spbu10.2024.309

Авторы

Фаррух Нуриддинович Дехконов Наманганский государственный университет, Узбекистан, 160136, Наманган, Уйчи ул., 316 https://orcid.org/0000-0003-4747-8557

DOI:

https://doi.org/10.21638/spbu10.2024.309

Аннотация

Ранее были рассмотрены некоторые задачи управления псевдопараболическим уравнением, не зависящие от инволюции. В данной работе рассматривается задача граничного управления, связанная с псевдопараболическим уравнением с инволюцией в ограниченной одномерной области. На части границы рассматриваемой области задано значение решения с функцией управления. Ограничения на управление задаются таким образом, чтобы среднее значение решения в рассматриваемой области получало заданное значение. Задача, заданная методом разделения переменных, сводится к интегральному уравнению Вольтерра второго рода. Существование функции управления доказано методом преобразования Лапласа.

Ключевые слова:

краевая задача, интегральное уравнение Вольтерра, функция управления, преобразование Лапласа, инволюция

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