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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Bibliographische Detailangaben
Datum:2018
1. Verfasser: Potapenko, Oleksii Yu.
Format: Artikel
Sprache:Russisch
Veröffentlicht: The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2018
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Online Zugang:http://journal.iasa.kpi.ua/article/view/150220
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Назва журналу:System research and information technologies

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System research and information technologies
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Zusammenfassung: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.