Some inverse problems in PDE’s in heart muscle fibers identification

I present some exact and approximate solutions of weak harmonic maps in two 
and three dimensions for the nonlinear Frank-Oseen equations from liquid crystal theory and 
their possible applications in the framework of non-invasive identification of the direction of muscle fibers in the human heart, as well as their striking similarity to certain structures in the field of astrophysics. It is a collaborative work with Nicolás Barnafi (Center for Mathematical Modeling, U. de Chile). If we have time, I present an apparently new numerical method (SOFIA) 
to compute null controls for the heat equation and applications to a source inverse problem, work in collaboration with Felipe Urrutia (MsC student at Mathematical Engineering Department, U. de Chile).