2024-03-29T08:10:11Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/697522022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116On decay rate of quenching profile at space infinity for axisymmetric mean curvature flowGiga, YoshikazuSeki, YukihiroUmeda, Noriakiat space infinityaxisymmetric mean curvature flow equationquenching profiledecay rate410We study the motion of noncompact hypersurfaces moved by their ean curvature obtained by a rotation around x-axis of the graph function y = u(x, t) (defined for all x 2 R). We are interested o estimate its profile when the hypersurface closes open ends at the uenching (pinching) time T. We estimate its profile at the quenching ime from above and below. We in particular prove that u(x, T) » xj¡a as jxj ! 1 if u(x, 0) tends to its infimum with algebraic rate xj¡2a (as jxj ! 1 with a > 0).Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69752info:doi/10.14943/84092https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69752/1/pre945.pdfHokkaido University Preprint Series in Mathematics9451112009-09-10engpublisher