The aim of this project is to carry out joint work with some members of the OCIAM at Oxford on some free boundary problems, mainly those coming from the modelling of dislocations.
We shall start by studying some two-dimensional models for arrays of screw and edge dislocations assumed to be infinitely long and parallel. The models are formulated in terms of the stress due to the dislocations and the boundary of the array, both of which are unknown, leading in this way to free boundary problems. We shall try to construct solutions for both the equilibrium and the evolution problem. Depending on progress on this issue, some three-dimensional models could also be studied.