A McKean–Vlasov equation with positive feedback and blow-ups
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 …
with positive feedback. As particles hit a barrier, they cause the other particles to jump in the …
Mean field systems on networks, with singular interaction through hitting times
S Nadtochiy, M Shkolnikov - The Annals of Probability, 2020 - JSTOR
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 …
Appl. 125 (2015) 2451–2492; Ann. Appl. Probab. 29 (2019) 89–129; Arch. Ration. Mech …
Classical solutions for a nonlinear Fokker-Planck equation arising in computational neuroscience
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 …
value problem for a nonlinear parabolic equation describing the collective behavior of an …
Global solutions to the supercooled Stefan problem with blow-ups: regularity and uniqueness
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 …
liquid, in one space dimension. A probabilistic reformulation of the problem allows us to …
Qualitative properties of solutions for the noisy integrate and fire model in computational neuroscience
JA Carrillo, B Perthame, D Salort, D Smets - Nonlinearity, 2015 - iopscience.iop.org
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 …
equation used to describe the activity of a homogeneous neural network characterized by its …
Contagious McKean--Vlasov problems with common noise: from smooth to singular feedback through hitting times
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 …
system of interacting particles on the positive half-line with common noise and feedback …
Uniqueness for contagious McKean–Vlasov systems in the weak feedback regime
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 …
have seen recent interest. Our first result shows that, in the weak feedback regime, there is …
McKean–Vlasov equations involving hitting times: Blow-ups and global solvability
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)≤ …
involving hitting times. Let (B (t); t≥ 0) be standard Brownian motion, and τ:= inf {t≥ 0: X (t)≤ …
Semi-analytical solution of a McKean–Vlasov equation with feedback through hitting a boundary
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 …
where the common drift depends on the rate of absorption of particles at a boundary. We …
[PDF][PDF] Mathematical models of some diffusive processes with free boundaries
A Fasano - SIMAI e-Lecture Notes, 2008 - cab.unime.it
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 …
relevant to industry, biology, medicine, environment, etc. Here a small selection of problems …