2024-03-29T01:46:33Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/838162022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116CRYSTALLINE SURFACE DIFFUSION FLOW FOR GRAPH-LIKE CURVESGIGA, MI-HOGIGA, YOSHIKAZUopen access410This 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.Department of Mathematics, Hokkaido University2022-01-13engdepartmental bulletin paperVoRhttps://doi.org/10.14943/100842http://hdl.handle.net/2115/8381610.14943/100842Hokkaido University Preprint Series in Mathematics1142135https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/83816/1/CrySurDiff.pdfapplication/pdf480.76 KB2022-01-13