Error analysis of finite element approximations of the inverse mean curvature flow arising from the general relativity

2007 ◽  
Vol 108 (1) ◽  
pp. 93-119 ◽  
Author(s):  
Xiaobing Feng ◽  
Michael Neilan ◽  
Andreas Prohl
Keyword(s):  
Finite Element ◽  
General Relativity ◽  
Error Analysis ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Finite Element Approximations ◽  
Inverse Mean Curvature Flow

scholarly journals Hyperbolic inverse mean curvature flow

2019 ◽  
Vol 70 (1) ◽  
pp. 33-66
Author(s):  
Jing Mao ◽  
Chuan-Xi Wu ◽  
Zhe Zhou
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Inverse Mean Curvature Flow

scholarly journals Life-Span of Classical Solutions to Hyperbolic Inverse Mean Curvature Flow

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Zenggui Wang
Keyword(s):  
Cauchy Problem ◽  
Life Span ◽  
Hyperbolic System ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Classical Solutions ◽  
Quasilinear Hyperbolic System ◽  
Inverse Mean Curvature Flow ◽  
The Cauchy Problem

In this paper, we investigate the life-span of classical solutions to hyperbolic inverse mean curvature flow. Under the condition that the curve can be expressed in the form of a graph, we derive a hyperbolic Monge–Ampère equation which can be reduced to a quasilinear hyperbolic system in terms of Riemann invariants. By the theory on the local solution for the Cauchy problem of the quasilinear hyperbolic system, we discuss life-span of classical solutions to the Cauchy problem of hyperbolic inverse mean curvature.

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