free boundary problems

Katerina Nik

Assistant Professor, Applied Mathematics and Computational Sciences

Partial Differential Equations free boundary problems calculus of variations Mathematical Biology Microelectromechanical fluid dynamics mean curvature flow

Professor Nik studies partial differential equations that describe phenomena in biological growth processes, fluid dynamics, and mechanical engineering.

Miguel Urbano

Professor, Applied Mathematics and Computational Sciences

nonlinear PDEs free boundary problems regularity theory

Professor Urbano’s research interests are in regularity theory for nonlinear partial differential equations, in particular of singular or degenerate type, arising from different applications, like phase transitions, flows in porous media or semi-supervised learning. He is also interested in free boundary problems, focusing on understanding the local behaviour of weak solutions and the geometric properties of interfaces.