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March/April 2013 Evolution of regular bent rectangles by the driven crystalline curvature flow in the plane with a non-uniform forcing term
Yoshikazu Giga, Przemyslaw Górka, Piotr Rybka
Adv. Differential Equations 18(3/4): 201-242 (March/April 2013).

Abstract

We study the motion of regular bent rectangles driven by singular curvature flow with a driving term. The curvature is being interpreted as a solution to a minimization problem. The evolution equation becomes in a local coordinate a system of Hamilton--Jacobi equations with free boundaries, coupled to a system of ODE's with nonlocal nonlinearities. We establish local-in-time existence of variational solutions to the flow, and uniqueness is proved under additional regularity assumptions on the data.

Citation

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Yoshikazu Giga. Przemyslaw Górka. Piotr Rybka. "Evolution of regular bent rectangles by the driven crystalline curvature flow in the plane with a non-uniform forcing term." Adv. Differential Equations 18 (3/4) 201 - 242, March/April 2013.

Information

Published: March/April 2013
First available in Project Euclid: 5 February 2013

zbMATH: 1295.35261
MathSciNet: MR3060195

Subjects:
Primary: 35K55 , 53C44

Rights: Copyright © 2013 Khayyam Publishing, Inc.

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Vol.18 • No. 3/4 • March/April 2013
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