Advances in Differential Equations

Evolution of regular bent rectangles by the driven crystalline curvature flow in the plane with a non-uniform forcing term

Yoshikazu Giga, Przemyslaw Górka, and Piotr Rybka

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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.

Article information

Source
Adv. Differential Equations Volume 18, Number 3/4 (2013), 201-242.

Dates
First available in Project Euclid: 5 February 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1360073016

Mathematical Reviews number (MathSciNet)
MR3060195

Zentralblatt MATH identifier
1295.35261

Subjects
Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.) 35K55: Nonlinear parabolic equations

Citation

Giga, Yoshikazu; Górka, Przemyslaw; Rybka, Piotr. Evolution of regular bent rectangles by the driven crystalline curvature flow in the plane with a non-uniform forcing term. Adv. Differential Equations 18 (2013), no. 3/4, 201--242. https://projecteuclid.org/euclid.ade/1360073016.


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