arXiv:1306.1406 Abstract | arXiv Analytics

arXiv:1306.1406 [math.AP]Abstract References Reviews Resources

Convergence to equilibrium of gradient flows defined on planar curves

Published 2013-06-06Version 1

We consider the evolution of open planar curves by the steepest descent flow of a geometric functional, under 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.

Categories: math.AP

Subjects: 53C44, 35K55

Keywords: gradient flows, convergence, stationary solution, equilibrium, steepest descent flow

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