Abstract
A front dynamics approach is developed to study the evolution of planar curves whose normal speed depends on curvature. The formulation is similar to Whitham’s shock dynamics theory for the propagation of shock wave in gases but assumes a different propagation rule. Equations that describe the motion of the front are obtained, and these are evolution equations for the normal direction and local arc length of the front. The solution of these equations leads to the front positions using an appropriate integration along rays. A similarity solution of the equations is found for the evolution of an initial corner. Free-boundary problems for the motion of a junction connecting front segments are discussed. A numerical method is presented to calculate the evolution of any number of front segments. The segments can be closed or open, connected to wall boundaries or not, or connected to other segments at 3-segment junctions. Several sample problems are considered to illustrate the method. An extension of the method for curvature-dependent motion under a constant area constraint is also discussed.
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