Mahir Hadžić: On generic melting rates for the Stefan problem

Stefan problem is one of the oldest free-boundary problems modelling phase transitions between liquids and solids. If, for example, the solid phase melts in finite time - this is an instance of singularity formation in the language of partial differential equations (PDE). If the rate of melting is self-similar we speak of Type I singularity formation.

After a brief introduction to the Stefan problem, I will show that for an open set of radial initial data the melting rate is to the leading order NOT given by the self-similar scaling. It is instead of Type II with rates predicted in the pioneering work of Herrero and Velazquez. Time remaining, I will explain what we expect to happen in non-radial setting. Our techniques rely on ideas from spectral theory, dynamical systems and PDE.

The lecture is organized jointly with Mathematics Colloquium. There will be snacks at the end of the talk.