90 citations · 142 across the 11 of their papers we have counts for
12 papers
Dilating blow-up time: A generalized solution of the NNLIF neuron model and its global well-posedness
Xu'an Dou, Zhennan Zhou
The nonlinear noisy leaky integrate-and-fire (NNLIF) model is a popular mean-field description of a large number of interacting neurons, which has attracted mathematicians to study…
A simplified voltage-conductance kinetic model for interacting neurons and its asymptotic limit
José A. Carrillo, Xu'an Dou, Zhennan Zhou
The voltage-conductance kinetic model for the collective behavior of neurons has been studied by scientists and mathematicians for two decades, but the rigorous analysis of its sol…
Bounds and long term convergence for the voltage-conductance kinetic system arising in neuroscience
Xu'An Dou, Benoît Perthame, Delphine Salort +1
The voltage-conductance equation determines the probability distribution of a stochastic process describing a fluctuation-driven neuronal network arising in the visual cortex. Its…
Exponential convergence to equilibrium for a two-speed model with variant drift fields via the resolvent estimate
Xu'an Dou, Zhennan Zhou
We study a two-speed model with variant drift fields, which generalizes the Goldstein-Taylor model but the two advection fields are not necessarily in proportion. Due to the lack o…
A tumor growth model with autophagy: the reaction-(cross-)diffusion system and its free boundary limit
Xu'an Dou, Jian-Guo Liu, Zhennan Zhou
In this paper, we propose a tumor growth model to incorporate and investigate the spatial effects of autophagy. The cells are classified into two phases: normal cells and autophagi…
Possible Chiral Topological Superconductivity in CrO bilayers
Xu Dou, Kangjun Seo, Bruno Uchoa
We address the possible emergence of spin triplet superconductivity in CrO bilayers, which are half-metals with fully spin-polarized conducting bands. Starting from a lattice…