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