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http://arks.princeton.edu/ark:/88435/dsp015x21tj73x
Title: | Stefan Problems with Supercooling: Theory and Applications |
Authors: | Baker, Graeme Scott |
Advisors: | Shkolnikov, Mykhaylo |
Contributors: | Applied and Computational Mathematics Department |
Keywords: | free boundary problems heat equation interacting particle systems mean-field interaction physical solutions supercooled Stefan problem |
Subjects: | Applied mathematics Mathematics |
Issue Date: | 2023 |
Publisher: | Princeton, NJ : Princeton University |
Abstract: | We consider certain McKean-Vlasov stochastic differential equations (SDEs) which arise as mean-field limits of particle systems with interactions through the hitting times of free boundaries. The interaction term in these equations is self-exciting, which can lead to short-time blowup in the form of jump discontinuities. Recently, such equations have found use as probabilistic representations for solutions of the supercooled Stefan problem, a free boundary partial differential equation (PDE), which describes the freezing of supercooled liquids; and they have also been used to model systemic risk in interconnected financial networks. In this work, we show existence of physical solutions for a two-phase version of this model: any possible discontinuities of these physical solutions must obey a natural physicality condition for the problem at hand. Additionally, we investigate the well-posedness of the one-phase problem by considering the sensitivity to perturbed boundary and initial conditions for physical solutions, as well as minimal solutions, another solution concept. |
URI: | http://arks.princeton.edu/ark:/88435/dsp015x21tj73x |
Type of Material: | Academic dissertations (Ph.D.) |
Language: | en |
Appears in Collections: | Applied and Computational Mathematics |
Files in This Item:
File | Description | Size | Format | |
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Baker_princeton_0181D_14698.pdf | 1.84 MB | Adobe PDF | View/Download |
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