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The classical Stefan problem and the vanishing surface tension limit

PDE and Applied Math Seminar

Speaker: Mahir Hadzic, MIT
Location: 1147 MSB
Start time: Tue, Apr 10 2012, 4:10PM

We develop a new unified framework for the treatment of well-posedness for the Stefan problem with and without surface tension. This is a well-known model describing solid-liquid phase transitions. Our approach yields new estimates for the regularity of the moving surface in the absence of surface tension, which allows us to prove that solutions of the Stefan problem with positive surface tension converge to solutions of the Stefan problem without surface tension. Our techniques rely on a fluid-mechanics inspired approach which, in a suitable sense, combines the Eulerian and the Lagrangian viewpoint. This is joint work with S. Shkoller.