Motion of a closed curve by minus the surface Laplacian of curvature
journal contributionposted on 01.01.1997 by Sergio A. Alvarez, Chun Liu
Any type of content formally published in an academic journal, usually following a peer-review process.
Abstract: "The phenomenon of surface diffusion is of interest in a variety of physical situations . 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 ╬│ contained in a tubular neighborhood of a fixed simple closed curve ╬│ΓéÇ 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[superscript h] of functions f whose Fourier transform (f╠é[subscript k])k[element of]Z decays faster than [absolute value of k][superscript -h], for h > 5. Our results are based on the machinery developed in , , , which allows the application of the method of maximal regularity , ,  in the spaces E[superscript h]."