THE CAUCHY PROBLEMS FOR DISSIPATIVE HYPERBOLIC MEAN CURVATURE FLOW

被引：0
|
作者：
Shixia Lv [1 ]
Zenggui Wang [1 ]
机构：
[1] School of Mathematical Sciences, Liaocheng University
来源：
AnnalsofAppliedMathematics | 2019年 / 35卷 / 02期
基金：
美国国家科学基金会;
关键词：
dissipative hyperbolic mean curvature flow; hyperbolic MongeAmpère equation; lifespan;
D O I：
暂无
中图分类号：
O186.1 [微分几何];
学科分类号：
摘要：
In this paper, we investigate initial value problems for hyperbolic mean curvature flow with a dissipative term. By means of support functions of a convex curve, a hyperbolic Monge-Amp`ere equation is derived, and this equation could be reduced to the first order quasilinear systems in Riemann invariants. Using the theory of the local solutions of Cauchy problems for quasilinear hyperbolic systems, we discuss lower bounds on life-span of classical solutions to Cauchy problems for dissipative hyperbolic mean curvature flow.
引用
收藏
页码：159 / 179
页数：21
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