Convex curves moving translationally in the plane |
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| Authors: | Chia-Hsing Nien |
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| Affiliation: | a Department of Applied Mathematics, Providence University, Taichung 43301, Taiwan
b Department of Mathematics, National Tsing Hua University, Hsinchu 30013, Taiwan |
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| Abstract: | We show that a nontrivial homothetic self-similar solution can happen only when F(k)=kα or F(k)=−k−α. We also derive a parametric representation of a translational self-similar solution. A translational self-similar solution may have self-intersections but cannot be a simple closed curve for any F(k). |
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| Keywords: | 35K15 35K55 |
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