The Allen-Cahn equation with weakly critical random initial datum

Simon Gabriel, Tommaso Rosati, Nikos Zygouras

This work considers the two-dimensional Allen-Cahn equation $$ \partial_t u = \frac{1}{2}Δu + \mathfrak{m}\, u -u^3\;, \quad u(0,x)= η(x)\;, \qquad \forall (t,x) \in [0, \infty) \t…