Hole-closing problems in fluid mechanics, heat conduction and mathematical biology (PLENARY)
by
Scott McCue
Mathematical Sciences, Queensland University of Technology

This talk relates to a class of moving boundary problems in which the governing equation applies outside a shrinking domain (the hole) bounded by a time-dependent simple closed curve in 2D or closed surface in 3D. In particular, it is of interest to track the shape of the hole, especially in the limit t→ t_c^-, where t_c is the time at which the hole closes. The goal of this talk will be to provide a flavour of the various issues that arise when dealing these sorts of moving boundary problems, focussing on the following three practical applications: bubble contraction in Hele-Shaw cells and porous media otherwise filled with viscous fluid; conduction-limited melting of dendritic crystals; and the mathematical modelling of epidermal wound healing.

Date received: December 16, 2009