| Abstract: |
| Diffuse interface models have attracted significant interest starting with the pioneering work of Cahn and Hilliard in 1958. In this talk, I will introduce and discuss examples of systems of Allen--Cahn and Cahn--Hilliard type perturbed by conservative noise, i.e., keeping the key mass conservation property, enjoyed by the deterministic counterparts of the systems, pathwise. The systems are endowed with a singular potential, as prescribed by the thermodynamical derivation of the model. In particular, results on existence and uniqueness of martingale and/or probabilistically-strong solutions are shown. The talk is based on joint works with Maurizio Grasselli (Politecnico di Milano), Andrea Papini (Chalmers University of Technology), Luca Scarpa (Politecnico di Milano) and Margherita Zanella (Politecnico di Milano). |
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