Differential and Integral Equations

Motion of a closed curve by minus the surface Laplacian of curvature

Sergio A. Alvarez and Chun Liu

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

The phenomenon of surface diffusion is of interest in a variety of physical situations [8]. Surface diffusion is modelled by a fourth-order quasilinear parabolic partial differential equation associated with the negative of the surface-Laplacian-of-curvature operator. We address the well-posedness of the corresponding initial value problem in the case in which the interface is a smooth closed curve $\Gamma$ contained in a tubular neighborhood of a fixed simple closed curve $\Gamma_0$ in the plane. We prove existence and uniqueness, as well as analytic dependence on the initial data of classical solutions of this problem locally in time, in the spaces $E^h$ of functions $f$ whose Fourier transform $(\hat f_k)_{k \in \bf Z}$ decays faster than $|k|^{-h}$, for $h > 5$. Our results are based on the machinery developed in [1], [2], and [3], which allows the application of the method of maximal regularity ([11], [14], and [4]) in the spaces $E^h$.

Article information

Source
Differential Integral Equations Volume 13, Number 10-12 (2000), 1583-1594.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356061141

Mathematical Reviews number (MathSciNet)
MR1787083

Zentralblatt MATH identifier
0974.35053

Subjects
Primary: 35R35: Free boundary problems
Secondary: 35K55: Nonlinear parabolic equations

Citation

Alvarez, Sergio A.; Liu, Chun. Motion of a closed curve by minus the surface Laplacian of curvature. Differential Integral Equations 13 (2000), no. 10-12, 1583--1594. https://projecteuclid.org/euclid.die/1356061141.


Export citation