期刊文献+

一类双曲平均曲率流的对称与整体解

Symmetries and Global Solutions for a Class of Hyperbolic Mean Curvature Flow
下载PDF
导出
摘要 该文讨论一类图(Graph)的双曲平均曲率流,它与Lagrangian型抛物平均曲率流密切相关.首先研究该平均曲率流的对称及其对称约化方程,得到若干常微分方程,进而讨论解的存在性;最后,研究具有一般形式的双曲平均曲率流的整体BV解、光滑解的爆破和整体存在性等. In this paper,we consider a class of one dimensional hyperbolic mean curvature flow,which is related to the Lagrangian parabolic mean curvature flow.First we derive the point Lie symmetries of this flow and obtain several ordinary differential equations.The existence of solutions is investigated.Finally,the global BV solutions,the lifespan for classical solutions and global existence of smooth solutions for this hyperbolic mean curvature flow are studied in detail.
作者 何春蕾 刘子慧 He Chunlei;Liu Zihui(School of Mathematics and Statistics,Anhui Normal University,Anhui Wuhu 241002)
出处 《数学物理学报(A辑)》 CSCD 北大核心 2022年第4期1089-1102,共14页 Acta Mathematica Scientia
基金 安徽省自然科学基金(2108085MA03)。
关键词 双曲平均曲率流 对称 整体解 解的爆破 Hyperbolic mean curvature flow Symmetry Global solution Blow up of solution
  • 相关文献

参考文献2

二级参考文献31

  • 1Albrecht A,Tuok,N.Evolution of cosmic string.Physics Review Letters,1985,54:1868-1871.
  • 2Alvarez L,Guichard F,Lions P L,Morel J M.Axioms and fundamental equations of image processing.Arch Rational Mech Anal,1993,123:199-257.
  • 3Angenent S,Gurtin M E.Multiplhase thermomechanics with an interfacial structure 2.evolution of an isothermal interface.Arch Rational Mech Anal,1989,108:323-391.
  • 4Cao F.Geometric Curve Evolution and Image Processing.Lecture Notes in Mathematics 1805.Berlin:Springer,2003.
  • 5Christodoulou D.Global solution of nonlinear hyperbolic equations for small initial data.Cornm Pure Appl Math,1986,39:367-282.
  • 6DeTurck D.Some regularity theorems in Riemannian geometry.Ann Scient Ecole Norm Sup Paris,1981,14:249-260.
  • 7Gage M,Hamilton R.The heat equation shrinking convex plane curves.J Diff Geom,1986,23:417-491.
  • 8Grayson M.Shortening embedded curves.Ann Math,1989,101:71-111.
  • 9Gurtin M E,Podio-Guidugli P.A hyperbolic theory for the evolution of plane curves.SIAM J Math Anal,1991,22:575-586.
  • 10Hadamard J.Le probléme de Cauchy et les èquations aux dérivées partielles linéaries hyperboliques.Paris:Hermann,1932.

共引文献4

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部