316 citations · 2.6k across the 149 of their papers we have counts for
6 papers · 2 filters
Convergence of a particle method for a regularized spatially homogeneous Landau equation
José A. Carrillo, Matias G. Delgadino, Jeremy S. H. Wu
We study a regularized version of the Landau equation, which was recently introduced in~\cite{CHWW20} to numerically approximate the Landau equation with good accuracy at reasonabl…
Existence of radial global smooth solutions to the pressureless Euler-Poisson equations with quadratic confinement
José A. Carrillo, Ruiwen Shu
We consider the pressureless Euler-Poisson equations with quadratic confinement. For spatial dimension , we give a necessary and sufficient condition for the exist…
Minimizers of 3D anisotropic interaction energies
José A. Carrillo, Ruiwen Shu
We study a large family of axisymmetric Riesz-type singular interaction potentials with anisotropy in three dimensions. We generalize some of the results of our recent work in two…
Interpreting systems of continuity equations in spaces of probability measures through PDE duality
José A. Carrillo, David Gómez-Castro
We introduce a notion of duality solution for a single or a system of transport equations in spaces of probability measures reminiscent of the viscosity solution notion for nonline…
Noise-driven bifurcations in a nonlinear Fokker-Planck system describing stochastic neural fields
José A. Carrillo, Pierre Roux, Susanne Solem
The existence and characterisation of noise-driven bifurcations from the spatially homogeneous stationary states of a nonlinear, non-local Fokker--Planck type partial differential…
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…