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Evolution d’une interface par diffusion de surface. (French) Zbl 0542.35078
The authors consider the evolution equation describing the motion of an interface due to surface diffusion. After some transformations they arrive at the following equation for the curvature K of the curve forming the interface: \[ \partial K/\partial t+\partial^ 2K/\partial s^ 4=- (\partial /\partial s)(K\int^{s}_{0}K(\partial^ 2K/\partial \delta^ 2)ds),\quad K(0,s)=k_ 0(s), \] where t stands for the time and s measures the arc-length along the curve. They then derive uniqueness and existence results along with some asymptotic properties.
Reviewer: R.Sperb

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B40 Asymptotic behavior of solutions to PDEs
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References:
[1] Baras P., I 295, in: C.R.Acad.Sc pp 611– (1982)
[2] Palais, R.S. 1968. ”Foundations of Global non linear analysis”. Benjamin. · Zbl 0164.11102
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