scholarly journals A variational formulation of anisotropic geometric evolution equations in higher dimensions

2008 ◽  
Vol 109 (1) ◽  
pp. 1-44 ◽  
Author(s):  
John W. Barrett ◽  
Harald Garcke ◽  
Robert Nürnberg
Keyword(s):  
Variational Formulation ◽  
Evolution Equations ◽  
Higher Dimensions ◽  
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.

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