一类双曲平均曲率流的对称与整体解

数学物理学报 ›› 2022, Vol. 42 ›› Issue (4): 1089-1102.

一类双曲平均曲率流的对称与整体解

何春蕾*(),刘子慧

安徽师范大学数学与统计学院安徽芜湖 241002

收稿日期:2021-08-31 出版日期:2022-08-26 发布日期:2022-08-08
通讯作者: 何春蕾 E-mail:hcl026@126.com
基金资助:
安徽省自然科学基金(2108085MA03)

Symmetries and Global Solutions for a Class of Hyperbolic Mean Curvature Flow

Chunlei He*(),Zihui Liu

School of Mathematics and Statistics, Anhui Normal University, Anhui Wuhu 241002

Received:2021-08-31 Online:2022-08-26 Published:2022-08-08
Contact: Chunlei He E-mail:hcl026@126.com
Supported by:
Anhui Provincial Natural Science Foundation(2108085MA03)

摘要/Abstract

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.

关键词: 双曲平均曲率流, 对称, 整体解, 解的爆破

Abstract:

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.

Key words: Hyperbolic mean curvature flow, Symmetry, Global solution, Blow up of solution

中图分类号:

O175.2

何春蕾,刘子慧. 一类双曲平均曲率流的对称与整体解[J]. 数学物理学报, 2022, 42(4): 1089-1102.

Chunlei He,Zihui Liu. Symmetries and Global Solutions for a Class of Hyperbolic Mean Curvature Flow[J]. Acta mathematica scientia,Series A, 2022, 42(4): 1089-1102.

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