ÍâÍøÌìÌÃ

We will discuss the segregation process of two immiscibleÌýsubstances (e.g., oil and water) that have been mixed together. In 1996,ÌýGiacomin and Lebowitz proposed a mathematical model for this process thatÌýcan be viewed as an alternative to the celebrated Cahn-Hilliard equation.ÌýThey also conjectured that, in their model, the first stage of the phaseÌýsegregation process, in which the mixture separates into two distinctÌýregions, can be captured on the large scale by a suitable free boundaryÌýproblem. I will describe the latter free boundary problem and some aspectsÌýof its analysis, and then explain how it arises in the context of theÌýGiacomin-Lebowitz model.