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.