13 citations · 16 across the 15 of their papers we have counts for
16 papers
Nonlinear Diffusion Equations: Full characterization of Entropies
Anton Arnold, Jose A. Carrillo, Daniel Matthes
This paper is concerned with the large-time behavior of quasilinear Fokker-Planck equations with confinement on the whole space . It aims at characterizing all relati…
Bridging Scales in Chemotaxis: Scale-Uniform Forward Stability for Run-and-Tumble Kernel Estimation
Jos{é} A. Carrillo, Jiangjun Ma, Min Tang
Chemotactic motion is described by run-and-tumble kinetic models at microscopic scales and by Keller--Segel equations at macroscopic scales. We develop variational loss functionals…
Non-uniqueness of weak solutions to cross-diffusion systems with advection
José A. Carrillo, Ansgar Jüngel, Jakub Skrzeczkowski +1
A cross-diffusion system with advection is considered on the whole line, describing the dynamics of two segregating population species. Starting from two initial densities supporte…
Stein Variational Gradient Descent dynamics for highly concentrated kernels
José A. Carrillo, Jakub Skrzeczkowski, Jethro Warnett
Stein Variational Gradient Descent (SVGD) is a widely used in practice algorithm for scalable sampling with deterministic particle updates. We study its behavior in the singular li…
A new formula for the Wasserstein distance between solutions to (nonlinear) continuity equations
José A. Carrillo, Piotr Gwiazda, Jakub Skrzeczkowski
Given two continuity equations with density-dependent velocities, we provide a new formula for the Wasserstein distance between the solutions in terms of the difference of velociti…
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…
Drift-diffusion equations with saturation
José Antonio Carrillo, Alejandro Fernández-Jiménez, David Gómez-Castro
We focus on a family of nonlinear continuity equations for the evolution of a non-negative density with a continuous and compactly supported nonlinear mobility …
Nonlocal particle approximation for linear and fast diffusion equations
José Antonio Carrillo, Antonio Esposito, Jakub Skrzeczkowski +1
We construct deterministic particle solutions for linear and fast diffusion equations using a nonlocal approximation. We exploit the -Wasserstein gradient flow structure of the…
Fisher-Rao Gradient Flow: Geodesic Convexity and Functional Inequalities
José A. Carrillo, Yifan Chen, Daniel Zhengyu Huang +2
The dynamics of probability density functions have been extensively studied in computational science and engineering to understand physical phenomena and facilitate algorithmic des…
Well-posedness of aggregation-diffusion systems with irregular kernels
José A. Carrillo, Yurij Salmaniw, Jakub Skrzeczkowski
We consider aggregation-diffusion equations with merely bounded nonlocal interaction potential . We are interested in establishing their well-posedness theory when the nonlocal…
Convergence and stability results for the particle system in the Stein gradient descent method
José A. Carrillo, Jakub Skrzeczkowski
There has been recently a lot of interest in the analysis of the Stein gradient descent method, a deterministic sampling algorithm. It is based on a particle system moving along th…
Convergence of a particle method for diffusive gradient flows in one dimension
J. A. Carrillo, F. S. Patacchini, P. Sternberg +1
We prove the convergence of a particle method for the approximation of diffusive gradient flows in one dimension. This method relies on the discretisation of the energy via non-ove…