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Existence of periodic solutions for equations of evolving curves
Title: | Existence of periodic solutions for equations of evolving curves |
Authors: | Giga, Y. Browse this author | Mizoguchi, N. Browse this author |
Issue Date: | Oct-1993 |
Publisher: | Department of Mathematics, Hokkaido University |
Journal Title: | Hokkaido University Preprint Series in Mathematics |
Volume: | 216 |
Start Page: | 1 |
End Page: | 45 |
Abstract: | Evolution equations of curvatures of convex curves are considered by the Gauss map parametrization. A time periodic unstable solution is constructed for a reasonable class of time periodic data. Our solution is arranged to satisfy a constraint so that it yields closed, embedded, convex curves moving periodically in time (up to . translation) .whose normal speed equals the curvature minus a given time periodic function depending on curves only through its normals. For curvatures of periodically evolving curves a priori lower and upper bounds depending only on periodic data are obtained. A new penalty method is introduced so that our solution satisfies the constraint. Solutions of penalized equations are constructed by adapting the degree theory. |
Type: | bulletin (article) |
URI: | http://hdl.handle.net/2115/68962 |
Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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