Final Public Oral Examination of Graeme Baker

Other
  • Graeme Baker
  • Princeton University
  • Stefan Problems with Supercooling: Theory and Applications
Jun 23, 2023
3 pm
Fine Hall 314

The Program in Applied and Computational Mathematics (PACM)

Announces

FINAL PUBLIC ORAL EXAMINATION OF

Graeme Baker   

DATE: FRIDAY, JUNE 23, 2023

Time: 3:00 PM (EDT)

Location: 314 FINE HALL  

_____________________________________________________

Stefan Problems with Supercooling: Theory and Applications

Advisor: Mykhaylo Shkolnikov 

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.

An electronic copy of Graeme’s dissertation is available per request; send an email to bwysocka@princeton.edu  

_____________________________________________________