14:30-15:30 Monday, 5 May 2025 Auditorium, Rectorate
Abstract
We consider the Allen–Cahn equation in the interval [−L, L] with Dirichlet boundary conditions, perturbed by a space–time white noise with intensity $\sqrt \epsilon$. Starting from the zero initial condition we study, in the limit $\epsilon\to0$ (with $L\to\infty$ suitably), the time and space scaling involved in the emergence of spatial patterns, where the solution is locally close to 1 or −1. These are determined by a smooth Gaussian process, that results from a convenient scaling of the linearised solution of the equation. Based in joint work with G. Valle and M. E. Vares.