Title: Onset of pattern formation for the stochastic Allen-Cahn equation

Wednesdays, December 16, at 3:30 p.m.  (Rio de Janeiro local time)

Spaker: Maria Eulalia Vares (IM-UFRJ)

Local: Sala C116 - Bloco C - Instituto de Matemática.

Abstract: We study the behavior of the solution of an Allen-Cahn equation with a double well reactive term under the action of a small space time white noise perturbation. We consider the SPDE with Dirichlet boundary conditions on a suitably large space interval starting from the identically null function that corresponds to the local maximum of the potential. Our main goal is the description, in the small noise limit, of the onset of the phase separation, with the emergence of spatial regions in each of the two phases. The time scale and the spatial structure are determined by a suitable Gaussian process that appears as the random counterpart of the linearized A-C equation. This issue was initially examined by De Masi et al. [Ann. Probab. {\bf 22}, (1994), 334-371] in the related context of a class of reaction-diffusion models obtained as a superposition of a speeded up stirring process and a spin flip dynamics.

Joint work with Stella Brassesco (IVIC-Caracas) and Glauco Valle (IM-UFRJ)