Abstract
This paper is concerned with the numerical approximation of mean curvature flow t! ( t) satisfying an additional inclusion-exclusion constraint 1 ( t) 2. Classical phase field model to approximate these evolving interfaces consists in solving the Allen-Cahn equation with Dirichlet boundary conditions. In this work, we introduce a new phase field model, which can be viewed as an Allen Cahn equation with a penalized double well potential. We first justify this method by a -convergence result and then show some numerical comparisons of these two dierent models. 1991 Mathematics Subject Classification. 49 Q, 35 B, 35 K.
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