Free boundary problems arise naturally in a range of mathematical models that describe physical, biological or financial phenomena, such as the melting of ice into water, the dynamics of a population or the behavior of stock markets, to mention just a few. They involve partial differential equations that are to be solved both for an unknown function and an unknown domain. We will discuss some free boundary problems and different approaches to tackle them.
Rafayel Teymurazyan obtained his PhD in Mathematics from the University of Lisbon (Portugal) in 2013. After postdoc and research positions at the Federal University of Ceará (Brazil), the University of Texas at Austin (USA) and the University of Coimbra (Portugal), he joined KAUST in May of 2023. He works on regularity theory for nonlinear PDEs and the mathematical analysis of free boundary problems.