Free boundary problems (FBPs) are concerned with the solution of a system of PDEs in a domain whose boundary is unknown in advance. As a part of the solution one needs to determine the (free) boundary of the domain. Classical FBPs include melting or solidification of materials, contact problem in elasticity, and fluid flows. The study of these problems led to the development of general theories, including the theory of variational inequalities and the regularity theory of the free boundary for variety of problems.
More recently new FBPs have emerged in mathematical biology, such as models arising from tumor growth, wound healing, and movement of cellular organisms.
The proposed workshop is, in a sense, a follow-up to the program on FBPs held at MSRI during the first half of 2011. The workshop will bring together researchers, including some who participated in that program, together with mathematical biologists who are working on FBPs arising in biology.
The aim of the workshop is to introduce a broad FBPs community to new free boundary problems that arise from significant biological processes, with the hope that the study of such problems will stimulate the development of new mathematical theories, as well as advance theoretical biology.