Speaker
Description
The interdisciplinary field of free-boundary problems – that is, problems arising in a wide variety of phenomena in nature, science and technology where the boundaries delimiting the domains are not known a priori and constitute unknowns to be determined – saw remarkable developments in their mathematical treatment during the last half a century.
Seeking to contextualise this class of problems within a little-known historical perspective, which traces back to classical problems, such as the shape of a rotating drop or a body of minimum resistance in a fluid, the solidification of the Earth or the melting of ice and the formation of crystals, filtration in porous media to contact problems involving solids, the diffusion of oxygen in living tissues to pattern formation, image recognition to optimal timing in financial processes, the mathematical treatment of interfaces and free-boundary problems ranges from modelling to mathematical analysis and from numerical calculation to computational simulation.
This talks reviews some of these problems, with a focus on the obstacle problem, Stefan’s problem and other phase-change problems, highlighting in particular some examples of the most significant contributions presented at the triennial conference series “Free Boundary Problems: Theory and Applications”.