zbMATH — the first resource for mathematics

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

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
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.