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Modified motion by mean curvature: local existence and uniqueness and qualitative properties. (English) Zbl 0994.35053

The authors study free boundary problems for modified motions by mean curvature, giving also examples of singular limits of some phase transition models. They prove an existence and uniqueness result for a time-local solution. They also give some properties of behaviors of the solutions.

MSC:

35K55 Nonlinear parabolic equations
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
35B65 Smoothness and regularity of solutions to PDEs
35R35 Free boundary problems for PDEs
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
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