| Abstract: |
| We introduce the concept of random separation property for stochastic phase-field models with singular potential. This consists in showing that almost every trajectory of the stochastic flow, with probability one, is detached from the potential barriers: the separation threshold depends on the trajectory itself and identifies thus a random variable. We illustrate the idea of the proof in the case of the stochastic Allen-Cahn equation, as well as qualitative properties of the random separation layer. Eventually, possible developments on the stochastic Cahn-Hilliard equation are also discussed.
The works presented in the talk are based on joint collaborations with Federico Bertacco (Imperial College London) and Carlo Orrieri (University of Pavia). |
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