Seminars

3pm Thursday 13 August 2009, Seminar room M345
School of Mathematical Sciences Colloquium
Developments in mathematical capillarity in the (no-more that) new millennium
Maria Athanassenas (Monash University)

Capillary surfaces are liquid-air or liquid-liquid interfaces, and are mathematically modelled as prescribed mean curvature surfaces -- a second order, nonlinear, elliptic PDE. I will present two topics in which there have been exciting developments since 2000:

(a) A new model incorporating compressibility has been introduced. I will describe how the prescribed mean curvature equation has changed, the results, and their similarities and differences to those of the incompressible model.

(b) I will give an overview of the resolved and open problems concerning behaviour in domains with corners.