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Existence of periodic solutions for equations of evolving curves

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83360

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
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

Submitter: 数学紀要登録作業用

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