13 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…
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…