4 papers
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…
A voltage-conductance kinetic system from neuroscience: probabilistic reformulation and exponential ergodicity
Xu'an Dou, Fanhao Kong, Weijun Xu +1
The voltage-conductance kinetic equation for an ensemble of neurons has been studied by many scientists and mathematicians, while its rigorous analysis is still at a premature stag…
An infinite-times renewal equation
Xu'An Dou, Benoît Perthame, Chenjiayue Qi +2
In neuroscience, the time elapsed since the last discharge has been used to predict the probability of the next discharge. Such predictions can be improved taking into account the…