Stochastic resonance in stochastic PDEs
A talk in the SPDEs, optimal control and mean field games series by
Nils Berglund from Orléans
| Abstract: | Stochastic resonance can occur when a multi-stable system is subject to both
periodic and random perturbations. For suitable parameter values, the system
can respond to the perturbations in a way that is close to periodic. This phenomenon
was initially proposed as an explanation for glacial cycles in the Earth's climate.
While its role in that context remains controversial, stochastic resonance has
since been observed in many physical and biological systems. This talk will
focus on stochastic resonance in parabolic SPDEs, such as the Allen-Cahn equation,
when they are driven by a periodic perturbation and by space-time white noise.
We will discuss both the case of one spatial dimension, in which the equation
is well-posed, and the case of two spatial dimensions, in which a renormalisation
procedure is required. This talk is based on joint works with Barbara Gentz
and Rita Nader. |