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Mathematical Physics Seminar

Mykhaylo Shkolnikov - A sharp interface limit in the Giacomin-Lebowitz model of phase segregation

Mykhaylo Shkolnikov

Location:  zoom
Date & time: Wednesday, 02 December 2020 at 10:45AM - 11:45AM

Mykhaylo Shkolnikov – Princeton University

 

Wednesday, December 2, 10:45AM

Title:
"A sharp interface limit in the Giacomin-Lebowitz model of phase segregation"

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 Cahn-Hilliard 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 Giacomin-Lebowitz model.