We propose a novel framework for analyzing the dynamics of distribution shift in real-world
systems that captures the feedback loop between learning algorithms and the distributions …

We show that degenerate nonlinear diffusion equations can be asymptotically obtained as a
limit from a class of nonlocal partial differential equations. The nonlocal equations are …

We study a nonlocal two species cross-interaction model with cross-diffusion. We propose a
positivity preserving finite volume scheme based on the numerical method introduced in [JA …

This paper studies the derivation of the quadratic porous medium equation and a class of
cross-diffusion systems from nonlocal interactions. We prove convergence of solutions of a …

Cell-cell adhesion is one the most fundamental mechanisms regulating collective cell
migration during tissue development, homeostasis, and repair, allowing cell populations to …

Structured population models are transport-type equations often applied to describe
evolution of heterogeneous populations of biological cells, animals or humans, including …

Taking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we
propose a convex formulation for each step of the JKO scheme for Wasserstein gradient …

Nonlocal cross-diffusion systems on the torus, arising in population dynamics and
neuroscience, are analyzed. The global existence of weak solutions, the weak–strong …

We propose a framework for two-player infinite-dimensional games with cooperative or
competitive structure. These games take the form of coupled partial differential equations in …

We investigate a class of systems of partial differential equations with nonlinear cross-
diffusion and nonlocal interactions, which are of interest in several contexts in social …