Return to Colloquia & Seminar listing
The classical Stefan problem and the vanishing surface tension limit
PDE & Applied Mathematics| Speaker: | Mahir Hadzic, MIT |
| Location: | 1147 MSB |
| Start time: | Tue, Apr 10 2012, 4:10PM |
Description
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.