Stefan problem: well-posedness and stability theories in presence and absence of surface tension

Add to your list(s) Download to your calendar using vCal

• Mahir Hadžić (MIT)
• Monday 28 January 2013, 15:00-16:00
• CMS, MR11.

If you have a question about this talk, please contact Clement Mouhot.

The Stefan problem is a well-known free boundary problem modeling phase transitions, melting/freezing phenomena, or nucleation. In the presence of surface tension, it serves as a micro-scale description of a phase transition, while in the absence thereof it acts as a macro-scale description. Mathematically, in the former case it has a flavor of a non-local curvature-driven flow, while in the latter case it changes its character into a non-linear system of parabolic-hyperbolic type, amenable to maximum principle techniques.

I will survey recent results on the well-posedness and stability theory, introducing a new unifying functional framework for the two problems. The first consequence is a rigorous vanishing surface tension limit. Moreover, I will show a global stability result in absence of surface tension, thereby explaining a hybrid methodology combining high-order energy methods and quantitative Hopf-type lemmas.

This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• CMS, MR11
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• Geometric Analysis and Partial Differential Equations seminar
• School of Physical Sciences

Note that ex-directory lists are not shown.