Existence of periodic solutions for equations of evolving curves

Giga, Y.; Mizoguchi, N.

Hokkaido University Preprint Series in Mathematics, 1993, 216, 1-45

Permalink : https://doi.org/10.14943/83360

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DOI	https://doi.org/10.14943/83360
URI	https://hdl.handle.net/2115/68962
タイトル	Existence of periodic solutions for equations of evolving curves
著者	著者名 Giga, Y.
著者	著者名 Mizoguchi, N.
言語	英語
発行日	1993-10
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	216
ページ	1-45
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record