5 papers
Numerical stationary states for nonlocal Fokker-Planck equations via fixed points of consistency maps
José A. Carrillo, Yurij Salmaniw, Antonio León Villares
We propose a fixed-point-based numerical framework for computing stationary states of nonlocal Fokker-Planck-type equations. Instead of discretising the differential operators dire…
Rate of Convergence for a Nonlocal-to-local Limit in One Dimension
José A. Carrillo, Charles Elbar, Stefano Fronzoni +1
We consider a nonlocal approximation of the quadratic porous medium equation where the pressure is given by a convolution with a mollification kernel. It is known that when the ker…
Evolution equations on co-evolving graphs: long-time behaviour and the graph continuity equation
José Antonio Carrillo, Antonio Esposito, László Mikolás
We focus on evolution equations on co-evolving, infinite, graphs and establish a rigorous link with a class of nonlinear continuity equations, whose vector fields depend on the gra…
Boundedness and stability of a 2-D parabolic-elliptic system arising in biological transport networks
Jose A. Carrillo, Bin Li, Li Xie
This paper is concerned with the Dirichlet initial-boundary value problem of a 2-D parabolic-elliptic system proposed to model the formation of biological transport networks. Even…
The Stein-log-Sobolev inequality and the exponential rate of convergence for the continuous Stein variational gradient descent method
José A. Carrillo, Jakub Skrzeczkowski, Jethro Warnett
The Stein Variational Gradient Descent method is a variational inference method in statistics that has recently received a lot of attention. The method provides a deterministic app…