A sharp interface limit in the GiacominLebowitz model of phase segregation
A sharp interface limit in the GiacominLebowitz model of phase segregation

Misha Shkolnikov, Princeton
We will discuss the segregation process of two immiscible substances (e.g., oil and water) that have been mixed together. In 1996, Giacomin and Lebowitz proposed a mathematical model for this process that can be viewed as an alternative to the celebrated CahnHilliard equation. They also conjectured that, in their model, the first stage of the phase segregation process, in which the mixture separates into two distinct regions, can be captured on the large scale by a suitable free boundary problem. I will describe the latter free boundary problem and some aspects of its analysis, and then explain how it arises in the context of the GiacominLebowitz model.