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 the …

Building on the line of work (Ann. Appl. Probab. 25 (2015) 2096–2133; Stochastic Process.
Appl. 125 (2015) 2451–2492; Ann. Appl. Probab. 29 (2019) 89–129; Arch. Ration. Mech …

In this paper we analyze the global existence of classical solutions to the initial boundary-
value problem for a nonlinear parabolic equation describing the collective behavior of an …

We consider the supercooled Stefan problem, which captures the freezing of a supercooled
liquid, in one space dimension. A probabilistic reformulation of the problem allows us to …

Abstract The Noisy Integrate-and-Fire equation is a standard non-linear Fokker–Planck
equation used to describe the activity of a homogeneous neural network characterized by its …

We consider a family of McKean-Vlasov equations arising as the large particle limit of a
system of interacting particles on the positive half-line with common noise and feedback …

We present a simple uniqueness argument for a collection of McKean–Vlasov problems that
have seen recent interest. Our first result shows that, in the weak feedback regime, there is …

This paper is concerned with the analysis of blow-ups for two McKean–Vlasov equations
involving hitting times. Let (B (t); t≥ 0) be standard Brownian motion, and τ:= inf {t≥ 0: X (t)≤ …

In this paper, we study the nonlinear diffusion equation associated with a particle system
where the common drift depends on the rate of absorption of particles at a boundary. We …

Diffusive phenomena including free boundaries occur in an impressive number of processes
relevant to industry, biology, medicine, environment, etc. Here a small selection of problems …