4 papers · 1 filter
On partial diffusion and mixing without hypoellipticity
Xu'an Dou, Delphine Salort, Didier Smets
A simple Markov process is considered involving a diffusion in one direction and a transport in a transverse direction. Quantitative mixing rate estimates are obtained with limited…
Noisy integrate-and-fire equation: continuation after blow-up
Xu'An Dou, Benoît Perthame, Delphine Salort +1
The integrate and fire equation is a classical model for neural assemblies which can exhibit finite time blow-up. A major open problem is to understand how to continue solutions af…
Classical solutions of a mean field system for pulse-coupled oscillators: long time asymptotics versus blowup
José Antonio Carrillo, Xu'an Dou, Pierre Roux +1
We introduce a novel reformulation of the mean-field system for pulse-coupled oscillators. It is based on writing a closed equation for the inverse distribution function associated…
Tumor growth with a necrotic core as an obstacle problem in pressure
Xu'an Dou, Chengfeng Shen, Zhennan Zhou
Motivated by the incompressible limit of a cell density model, we propose a free boundary tumor growth model where the pressure satisfies an obstacle problem on an evolving domain…