3 papers
math.PR2026
The supercooled Stefan problem with transport noise: weak solutions and blow-up
Sean Ledger, Andreas Sojmark
We derive two weak formulations for the supercooled Stefan problem with transport noise on a half-line: one captures a continuously evolving system, while the other resolves blow-u…
math.PR2024
At the Mercy of the Common Noise: Blow-ups in a Conditional McKean--Vlasov Problem
Sean Ledger, Andreas Sojmark
We extend a model of positive feedback and contagion in large mean-field systems, by introducing a common source of noise driven by Brownian motion. Although the driving dynamics a…
math.PR2024
A McKean--Vlasov equation with positive feedback and blow-ups
Ben Hambly, Sean Ledger, Andreas Sojmark
We study a McKean--Vlasov equation arising from a mean-field model of a particle system with positive feedback. As particles hit a barrier they cause the other particles to jump in…