At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …

An algebraic decay rate is derived which bounds the time required for velocities to
equilibrate in a spatially homogeneous flow-through model representing the continuum limit …

A simple model to handle the flow of people in emergency evacuation situations is
considered: at every point x, the velocity U (x) that individuals at x would like to realize is …

In this paper, we provide an analytical framework for investigating the efficiency of a
consensus-based model for tackling global optimization problems. This work justifies the …

Variational steepest descent approximation schemes for the modified Patlak–Keller–Segel
equation with a logarithmic interaction kernel in any dimension are considered. We prove …

We investigate nonlocal interaction equations with repulsive–attractive radial potentials.
Such equations describe the evolution of a continuum density of particles in which they …

The aim of this paper is to discuss the effects of linear and nonlinear diffusion in the large
time asymptotic behavior of the Keller–Segel model of chemotaxis with volume filling effect …

We consider the non-nonlinear optimal transportation problem of minimizing the cost
functional C_∞(λ)=λ-ess\,sup_(x,y)∈Ω^2|yx| in the set of probability measures on Ω^2 …

The aim of this paper is to establish rigorous results on the large time behavior of nonlocal
models for aggregation, including the possible presence of nonlinear diffusion terms …

We study certain nonlinear continuous models of opinion formation derived from a kinetic
description involving exchanges of opinion between individual agents. These models imply …