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The supercooled Stefan problem
Multi angle
Authors : Shkolnikov, Mykhaylo (Author of the conference)
CIRM (Publisher )
35B05 - "General behavior of solutions of PDE (comparison theorems; oscillation, zeros and growth of solutions; mean value theorems)"
60H30 - Applications of stochastic analysis (to PDE, etc.)
80A22 - Stefan problems, phase changes, etc.
35B44 - Blow-up (PDE)
Additional resources :
https://www.cirm-math.fr/RepOrga/2104/Slides/Shkolnikov.pdf
CIRM (Publisher )
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Abstract :
We will consider the supercooled Stefan problem, which captures the freezing of a supercooled liquid, in one space dimension. A probabilistic reformulation of the problem allows to define global solutions, even in the presence of blow-ups of the freezing rate. We will provide a complete description of such solutions, by relating the temperature distribution in the liquid to the regularity of the ice growth process. The latter is shown to transition between (i) continuous differentiability, (ii) Holder continuity, and (iii) discontinuity. In particular, in the second regime we rediscover the square root behavior of the growth process pointed out by Stefan in his seminal paper [Ste89] from 1889 for the ordinary Stefan problem. In our second main theorem, we will establish the uniqueness of the global solutions, a first result of this kind in the context of growth processes with singular self-excitation when blow-ups are present. Based on joint work with Francois Delarue and Sergey Nadtochiy.
MSC Codes : 35B05 - "General behavior of solutions of PDE (comparison theorems; oscillation, zeros and growth of solutions; mean value theorems)"
60H30 - Applications of stochastic analysis (to PDE, etc.)
80A22 - Stefan problems, phase changes, etc.
35B44 - Blow-up (PDE)
Additional resources :
https://www.cirm-math.fr/RepOrga/2104/Slides/Shkolnikov.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 09/05/2019 Conference Date : 12/04/2019 Subseries : Research talks arXiv category : Probability ; Mathematical Physics ; Analysis of PDEs Mathematical Area(s) : Mathematical Physics ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:56:24 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-04-12_Shkolnikov.mp4 
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Information on the Event
Event Title : Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial DataEvent Organizers : Basor, Estelle ; Bufetov, Alexander ; Cafasso, Mattia ; Grava, Tamara ; McLaughlin, Ken Dates : 08/04/2019 - 12/04/2019 Event Year : 2019 Event URL : https://www.chairejeanmorlet.com/2104.html
Citation Data
DOI : 10.24350/CIRM.V.19517903Cite this video as: Shkolnikov, Mykhaylo (2019). The supercooled Stefan problem. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19517903 URI : http://dx.doi.org/10.24350/CIRM.V.19517903 |
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