Numerical approximation of anisotropic geometric evolution equations in the plane

2007 ◽  
Vol 28 (2) ◽  
pp. 292-330 ◽  
Author(s):  
J. W. Barrett ◽  
H. Garcke ◽  
R. Nurnberg
Keyword(s):  
Numerical Approximation ◽  
Evolution Equations ◽  
Geometric Evolution Equations ◽  
Geometric Evolution

scholarly journals A short proof of backward uniqueness for some geometric evolution equations

2016 ◽  
Vol 27 (12) ◽  
pp. 1650102 ◽  
Author(s):  
Brett Kotschwar
Keyword(s):  
Evolution Equations ◽  
Short Proof ◽  
Direct Proof ◽  
Uniqueness Of Solutions ◽  
Logarithmic Convexity ◽  
Geometric Evolution Equations ◽  
Carleman Inequalities ◽  
Geometric Evolution ◽  
Backward Uniqueness ◽  
Energy Quantity

We present a simple, direct proof of the backward uniqueness of solutions to a class of second-order geometric evolution equations which includes the Ricci and cross-curvature flows. The proof, based on a classical argument of Agmon–Nirenberg, uses the logarithmic convexity of a certain energy quantity in the place of Carleman inequalities. We further demonstrate the applicability of the technique to the [Formula: see text]-curvature flow and other higher-order equations.

Sign in / Sign up

Export Citation Format

Share Document