2000 Motion of a closed curve by minus the surface Laplacian of curvature
Sergio A. Alvarez, Chun Liu
Differential Integral Equations 13(10-12): 1583-1594 (2000). DOI: 10.57262/die/1356061141


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 $E^h$.


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Sergio A. Alvarez. Chun Liu. "Motion of a closed curve by minus the surface Laplacian of curvature." Differential Integral Equations 13 (10-12) 1583 - 1594, 2000. https://doi.org/10.57262/die/1356061141


Published: 2000
First available in Project Euclid: 21 December 2012

zbMATH: 0974.35053
MathSciNet: MR1787083
Digital Object Identifier: 10.57262/die/1356061141

Primary: 35R35
Secondary: 35K55

Rights: Copyright © 2000 Khayyam Publishing, Inc.


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Vol.13 • No. 10-12 • 2000
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