TY - JOUR
T1 - Convergence to equilibrium of gradient flows defined on planar curves
AU - Novaga, Matteo
AU - Okabe, Shinya
N1 - Funding Information:
The second author was partially supported by the JSPS Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation and by Grant-in-Aid for Young Scientists (B) (No. 24740097).
Publisher Copyright:
© 2015 De Gruyter.
PY - 2017
Y1 - 2017
N2 - We consider the evolution of open planar curves by the steepest descent flow of a geometric functional, with different boundary conditions. We prove that, if any set of stationary solutions with fixed energy is finite, then a solution of the flow converges to a stationary solution as time goes to infinity. We also present a few applications of this result.
AB - We consider the evolution of open planar curves by the steepest descent flow of a geometric functional, with different boundary conditions. We prove that, if any set of stationary solutions with fixed energy is finite, then a solution of the flow converges to a stationary solution as time goes to infinity. We also present a few applications of this result.
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U2 - 10.1515/crelle-2015-0001
DO - 10.1515/crelle-2015-0001
M3 - Article
AN - SCOPUS:84990189953
SN - 0075-4102
VL - 2017
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 733
ER -