Последние результаты для уравнения Кана - Хиллиарда с динамической границей

В статье рассматривается уравнение Кана - Хиллиарда 'чистое' или с вязкостью с возможно сингулярными потенциалами и динамическими граничными условиями. Обсуждается корректность соответствующей начальной задачи. Изучается задача граничного управления для системы Кана - Хиллиарда с вязкостью и находятся необходимые условия оптимальности первого порядка. Кроме того, ставится аналогичная задача граничного управления для 'чистой' системы Кана - Хиллиарда, результаты получаются помощью предельного перехода в случае системы Кана - Хиллиарда с вязкостью, когда коэффициент вязкости стремится к нулю.

Ключевые слова

уравнение Кана - Хиллиарда; динамические граничные условия; разделение фаз; корректность; оптимальное граничное управление; условия оптимальности.

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