Formation of singularities in the motion of plane curves under hyperbolic mean curvature flow

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:247

Article

Kong, De-Xing²  Wang, Zeng-Gui¹ 

[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[2] Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China

关键词: Hyperbolic mean curvature flow;    Quasilinear wave equation;    First-order hyperbolic system;    Singularity;    Life-span;   

DOI  :  10.1016/j.jde.2009.04.016

来源: Elsevier

【 摘 要 】

This paper concerns the hyperbolic mean curvature flow (HMCF) for plane curves. A quasilinear wave equation is derived and studied for the motion of plane curves under the HMCF. Based on this, we investigate the formation of singularities in the motion of these curves. In particular, we prove that the motion under the HMCF of periodic plane curves with small variation on one period and small initial velocity in general blows up and singularities develop in finite time. Some blowup results have been obtained and the estimates on the life-span of the solutions are given. (C) 2009 Published by Elsevier Inc.

【 授权许可】

Free