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A Billiard-Based Game Interpretation of the Neumann Problem for the Curve Shortening Equation
Title: | A Billiard-Based Game Interpretation of the Neumann Problem for the Curve Shortening Equation |
Authors: | Giga, Yoshikazu Browse this author | Liu, Qing Browse this author |
Issue Date: | 2008 |
Publisher: | Department of Mathematics, Hokkaido University |
Journal Title: | Hokkaido University Preprint Series in Mathematics |
Volume: | 922 |
Start Page: | 1 |
End Page: | 40 |
Abstract: | This paper constructs a family of discrete games, whose value functions converge to the unique viscosity solution of the Neumann boundary problem of the curve shortening flow equation. To derive the boundary condition, a billiard semiflow is introduced and its basic properties near the boundary are studied for convex and more general domains. It turns out that Neumann boundary problems of mean curvature flow equations can be intimately connected with purely deterministic game theory. |
Type: | bulletin (article) |
URI: | http://hdl.handle.net/2115/69729 |
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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