English
The supercooled Stefan problem
Multi angle
Auteurs : Shkolnikov, Mykhaylo (Auteur de la Conférence)
CIRM (Editeur )
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)
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2104/Slides/Shkolnikov.pdf
CIRM (Editeur )
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Résumé :
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.
Codes MSC : 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)
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2104/Slides/Shkolnikov.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 09/05/2019 Date de captation : 12/04/2019 Sous collection : Research talks arXiv category : Probability ; Mathematical Physics ; Analysis of PDEs Domaine : Mathematical Physics ; Probability & Statistics Format : MP4 (.mp4) - HD Durée : 00:56:24 Audience : Researchers Download : https://videos.cirm-math.fr/2019-04-12_Shkolnikov.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial DataOrganisateurs de la rencontre : Basor, Estelle ; Bufetov, Alexander ; Cafasso, Mattia ; Grava, Tamara ; McLaughlin, Ken Dates : 08/04/2019 - 12/04/2019 Année de la rencontre : 2019 URL Congrès : https://www.chairejeanmorlet.com/2104.html
Données de citation
DOI : 10.24350/CIRM.V.19517903Citer cette vidéo: 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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