The Role of Symmetry and Separation in Surface Evolution and Curve Shortening

title={The Role of Symmetry and Separation in Surface Evolution and Curve Shortening},
author={Philip Broadbridge and Peter J. Vassiliou},
journal={Symmetry Integrability and Geometry-methods and Applications},
year={2011},
volume={7},
pages={052}
}
• Published 1 June 2011
• Mathematics, Physics
• Symmetry Integrability and Geometry-methods and Applications
With few exceptions, known explicit solutions of the curve shortening flow (CSE) of a plane curve, can be constructed by classical Lie point symmetry reductions or by functional separation of variables. One of the functionally separated solutions is the exact curve shortening flow of a closed, convex \oval"-shaped curve and another is the smoothing of an initial periodic curve that is close to a square wave. The types of anisotropic evaporation coefficient are found for which the evaporation…
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