University of Toronto
                  PDE/Applied Math/Analysis Seminar
                    Friday 26 September, 12:10-1:00pm
                          6183 Bahen Center      



SPEAKER:  Marianne Korten 

TITLE:    On the Stefan and Hele-Shaw problems with a degenerate phase

ABSTRACT: In this talk I will survey new results about parabolic 
          free boundary problems with a degenerate phase connected to
          Stefan problems.  The first one establishes the Rankine-Hugoniot 
          condition at "most" points of the free boundary in the one 
          phase Stefan problem under minimal smoothness assumptions 
          (joint work with Donatella Danielli).  

          The second one establishes intrinsic energy estimates for the 
          temperature in the two phase Stefan problem (which are more 
          delicate to obtain as one is working with signed solutions). 
          Immediate applications are explicit expressions for the
          free boundary measures, leading to an existence theorem for 
          the two-phase Stefan problem when initial data are
          signed measures (joint work with Chuck Moore).
 
          Next I will describe complete existence and uniqueness results 
          for the Hele-Shaw problem in higher dimensions  with a degenerate 
          phase,  which hold even for a non-simply connected injection slot. 
          These results cover both Dirichlet and Neumann boundary data and 
          include classical results under enough regularity. Under standard 
          assumptions we obtain regularity results for the free boundary 
          (joint work with Ivan Blank and Chuck Moore).


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University of Toronto PDE/Applied Math/Analysis Seminar 
http://www.math.toronto.edu/appmath/

2006-2007 organizers:
          Pieter Blue           pblue@ math.toronto.edu
          Almut Burchard        almut@ math.toronto.edu
          Robert McCann		mccann@ math.toronto.edu
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