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math.AP2009★ 1 cited
Convergence of perturbed Allen-Cahn equations to forced mean curvature flow
Luca Mugnai, Matthias Röger
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-i…
math.AP2007★ 3 cited
The Allen-Cahn Action functional in higher dimensions
Luca Mugnai, Matthias Röger
The Allen-Cahn action functional is related to the probability of rare events in the stochastically perturbed Allen-Cahn equation. Formal calculations suggest a reduced action func…