Metastability for small random perturbations of a PDE with blow-up

GROISMAN, PABLO; SAINTIER, NICOLAS; SAGLIETTI, SANTIAGO

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2018 vol. 128 p. 1558 - 1589

0304-4149

We study random perturbations of a reaction?diffusion equation with a unique stable equilibrium and solutions that blow-up in finite time. If the strength of the perturbation ε>0 is small and the initial data is in the domain of attraction of the stable equilibrium, the system exhibits metastable behavior: its time averages remain stable around this equilibrium until an abrupt and unpredictable transition occurs which leads to explosion in a finite time (but exponentially large in ε−2). Moreover, for initial data in the domain of explosion we show that the explosion times converge to the one of the deterministic solution.