Convergence of perturbed Allen-Cahn equations to forced mean curvature flow
Luca MugnaiMatthias Roeger
53C4435K5549Q15Allen-Cahn equationsharp interface limitsmotion by mean curvature
We study perturbations of the Allen-Cahn equation and prove the convergence to forced mean curvature flow in the sharp interface limit. We allow for perturbations that are square-integrable with respect to the diffuse surface area measure. We give a suitable generalized formulation for forced mean curvature flow and apply previous results for the Allen-Cahn action functional. Finally, we discuss some applications.
Indiana University Mathematics Journal
2011
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10.1512/iumj.2011.60.3949
10.1512/iumj.2011.60.3949
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Indiana Univ. Math. J. 60 (2011) 41 - 76
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