What is a Free Boundary?

A seminar to be conducted by Dr. Henrik Shahgholian, the Royal Institute of Technology, Stockholm, Sweden

Abstract: The term Free Boundary Problems (FBP) refers to a class of problems in which one or several variables must be determined in different and a priori unknown domains of the space, or space-time. Hence, finding the domain is part of the problem. The process is usually controlled by several underlying mathematical conditions that are derived from certain physical laws or other constraints governing a phase transition. FBs arise in various mathematical models encompassing applications that ranges from physical to economics, financial and biological phenomenon, where there is an extra effect of the medium. This effect is in general a qualitative change of the medium and hence an appearance of a phase transition: ice to water, liquid to crystal, buying to selling (assets), active to inactive (biology), blue to red (coloring games), disorganized to organized (self-organizing criticality), etc. The boundary between these two states are called free boundaries, and are a priori unknown. I shall discuss some of these models from a mathematical point of view, in a very general framework, and mention some results and methodology.

The talk will be at an introductory level and accessible to larger audience.

Speaker: Dr. Henrik Shahgholian received his PhD degree in partial differential equations from the Royal Institute of Technology, Stockholm (Sweden) in 1991. He is currently a full professor at the same institute and is a well-established researcher in the field of partial differential equations, with more than 100 publications in top journals, grants and awards from various academies around the world or invited positions in top places.

For more information, please contact cenache@aus.edu.