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CRYSTALLINE SURFACE DIFFUSION FLOW FOR GRAPH-LIKE CURVES

GIGA, MI-HO GIGA, YOSHIKAZU 北海道大学

2022.01.13

概要

This paper studies a fourth-order crystalline curvature ow for a curve represented by the graph of a spatially periodic function. This is a spe-cial example of general crystalline surface diffusion flow. We consider a special class of piecewise linear functions and calculate its speed. We introduce notion of firmness and prove that the solution stays firm if initially it is firm at least for a short time. We also give an example that a facet (flat part) may split if the initial profile is not firm. Moreover, an example of facet-merging is given as well as several estimates for the speed of each facet.

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(M.-H. Giga) GRADUATE SCHOOL OF MATHEMATICAL SCIENCES, THE UNIVERSITY OF TOKYO, 3-8-1 KOMABA, MEGURO-KU, TOKYO 153-8914, JAPAN E-mail address: mihogiga@ms.u-tokyo.ac.jp

(Y. Giga) GRADUATE SCHOOL OF MATHEMATICAL SCIENCES, THE UNIVERSITY OF TOKYO, 3-8-1 KOMABA, MEGURO-KU, TOKYO 153-8914, JAPAN E-mail address: labgiga@ms.u-tokyo.ac.jp

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