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},
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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    Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
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