7 papers
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…
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…
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…
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…