Free boundary problems are today considered as one of the most important directions in the mainstream of the analysis of partial differential equations (PDEs), with an abundance of applications in various sciences and real world problems. In the last two decades, various new ideas, techniques, and methods have been developed, and new important, challenging problems in physics, engineering, industry, finance, biology, and other areas have arisen.
The topics of this programme are at the forefront of current exciting developments. We realise that there have been few activities on free boundary problems in recent decades in the UK. We strongly believe that a thematic programme at the Newton Institute will have a huge impact on the development of FBPs from all points of view. The programme is directed towards theory, numerics and applications. It will further enhance the interaction between UK mathematicians and top international researchers in this field and strengthen the UK expertise in FBPs.
The study of free boundary problems is an extremely broad topic due to the abundance of applications. This breadth presents challenges and opportunities! Many problems treated by applied scientists and numerical analysts are not well known amongst theoretical people, and vice versa. This leads to the development of the topic in different directions and sometimes with no links. However, often there are several unifying themes with respect to methodologies and techniques. The aim of programme is to enhance those links and unifying techniques by bringing together the relevant specialists. Common approaches for existence theory are sub- and supersolution techniques, minimisation, variational methods, inverse function theory, complex function theory, iteration, and regularisation. Numerical schemes are often based and/or analysed using these ideas.