PDE problems arising in mathematical biology

Recent years have seen a dramatic increase in mathematical models of biological processes that are described in terms of systems of partial differential equations. In this talk I will give some examples of such models and discuss the mathematical challenges that arise in the analysis of these systems. Examples include cancer models as  free boundary problems for  systems of elliptic-parabolic-hyperbolic equations; a wound healing process modeled by means of Stokes equation with a free boundary, and a reaction-hyperbolic system which arises in the movement of neurofilaments in axons.  Recent results and open questions will be described.