PDE seminar, May 26th 2016
Thursday 26th EHESS, 190-198 Avenue de France, room 466, 4th floor - 75013 Paris
11h00 : Adriano Pisante (Université Sapienza de Rome, chercheur invité à l'Ecole Normale Supérieure)
Singular limits for the perturbed Allen-Cahn equation: mean curvature flow, action functional and large deviations
We consider the sharp interface limit for the Allen-Cahn equation on the three dimensional torus with deterministic initial condition and deterministic or stochastic forcing terms. In the deterministic case, we discuss the convergence of solutions to the mean curvature flow, possibly with a forcing term, in the spirit of the pioneering work of Tom Ilmanen (JDG '93). In addition we analyze the convergence of the corresponding action functionals to a limiting functional described in terms of varifolds. If time permits, I will also comment on related results for the stochastic case, describing how this limiting functional enters in the large deviation asymptotics for the laws of the corresponding processes in the joint sharp interface and small noise limit.
We consider the sharp interface limit for the Allen-Cahn equation on the three dimensional torus with deterministic initial condition and deterministic or stochastic forcing terms. In the deterministic case, we discuss the convergence of solutions to the mean curvature flow, possibly with a forcing term, in the spirit of the pioneering work of Tom Ilmanen (JDG '93). In addition we analyze the convergence of the corresponding action functionals to a limiting functional described in terms of varifolds. If time permits, I will also comment on related results for the stochastic case, describing how this limiting functional enters in the large deviation asymptotics for the laws of the corresponding processes in the joint sharp interface and small noise limit.
Poster here