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Stefan problem: well-posedness and stability theories in presence and absence of surface tension
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.
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Other listsNatural History Cabinet, Cambridge University Department of History and Philosophy of Science Collaborative research symposium. Funding available for collaborative research out of Science and Technology Funding Council areas. Earthwatch Lecture
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