Mathematics Colloquium: On the two-phase Stefan problem
4:10 p.m. Murrow 55
Dr. Charles N. Moore
We consider the two-phase Stefan problem ut = (u) where (u) = u + 1 for u < âˆ’1, (u) = 0 for âˆ’1 u 1, and (u) = u âˆ’ 1 for u > 1. This models the flow of heat within a substance which can be in a liquid phase or a solid phase, and for which there is a latent heat to initiate phase change. This allows for the presence of a region which is between the liquid and solid phases. We discuss existence and uniqueness of solutions of the Cauchy problem, energy estimates and regularity of solutions. We also discuss the problem ut = (u) for other functions . I will also take a few minutes to mention some of my other work: probabilistic behavior in harmonic analysis, and acceleration of Fourier series.