Приклад дослідження коректності крайових задач на основі методу дифеоморфізмів

The search for methods for checking correctness of boundary value problems in spaces of an infinite-dimensional argument is one of the problems of the infinite-dimensional analysis. In this paper, the author proposed a method to broaden the class of correct problems by reducing them to already previ...

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Збережено в:
Бібліографічні деталі
Дата:2018
Автор: Potapenko, Oleksii Yu.
Формат: Стаття
Мова:Російська
Опубліковано: The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2018
Теми:
Онлайн доступ:http://journal.iasa.kpi.ua/article/view/150220
Теги: Додати тег
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Назва журналу:System research and information technologies

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System research and information technologies
Опис
Резюме:The search for methods for checking correctness of boundary value problems in spaces of an infinite-dimensional argument is one of the problems of the infinite-dimensional analysis. In this paper, the author proposed a method to broaden the class of correct problems by reducing them to already previously considered "canonical type" problems. The reduction process consists of searching for a special class diffeomorphism between Riemannian manifolds, areas in Hilbert’s space among them, which allows to reduce the problem to a simpler one. Boundary value problems are considered in "L2-version". This paper provides an example of such a problem. To fulfill the example, Fréchet derivatives of the diffeomorphism and the inverse mapping are found; diffeomorphism boundedness — a condition of the theorem about a boundary value problem associated with diffeomorphism applicability — is proved.