## UC Berkeley / Lawrence Berkeley Laboratory

#### The heat flow for director fields

**Michiel Bertsch, University of Rome**

##### February 18th, 2010 at 2PM–3PM in 740 Evans Hall [Map]

Parabolic equations for vectors with constant norm arise naturally in
applications (magnetism, liquid crystals, etc.). In this talk I focus on the
mathematical properties of the basic heat equation, neglecting the reaction
terms determined by specific applications. The nonlinear constraint of constant
norm leads to solutions which may have singularities, and solutions are not
always uniquely determined by their initial and boundary values. Through a
review of results we shall discuss some challenging open problems.