Some research perspectives on stochastic diffuse interface models
A talk in the SPDEvent series by
Andrea Di Primio from Politecnico di Milano
| Abstract: | The dynamics of multicomponent systems play a central role in various applied fields, ranging from Materials Science to Biology. From the mathematical standpoint, a first theoretical framework for modelling such systems was established by J. W. Cahn and J. E. Hilliard in 1958, through the introduction of the so-called diffuse interface approach, which describes phase separation processes via systems of partial differential equations. Later, in 1970, recognising the importance of rendering thermal fluctuations and microscopic effects, H. E. Cook proposed a stochastic version of the Cahn-Hilliard model, laying the groundwork for the study of stochastic diffuse interface models. In this talk, I will present some recent results in the field of diffuse interface models, mainly concerned with existence and uniqueness of solutions, as well as with their long-time behaviour in terms of the theory of invariant measures. Some open problems will also be addressed, in order to give some insights on current and future research on the topic. |