159 citations · 301 across the 35 of their papers we have counts for
40 papers
Nonlinear kinetic Fokker-Planck equations: existence and diffusion limits
Emeric Bouin, Jean Dolbeault, Antoine Mellet
In this paper, we focus on a new type of non-linear kinetic Fokker-Planck equation where the non-linearity comes from a non-linear diffusion in the velocity variable. The existence…
Cell-cell adhesion and multiphase Hele-Shaw problem as the singular limit of a Keller-Segel system
Jiwoong Jang, Antoine Mellet
We investigate a singular limit of a system of Patlak-Keller-Segel (PKS) equations modeling the evolution of multiple interacting species. Our primary motivation is the Differentia…
Range expansion by growth and congestion
Henri Berestycki, Antoine Mellet
We introduce here a nonlinear and nonlocal model that describes the range expansion of a population resulting from growth and competition for space. This type of phenomenon underli…
Constrained hydrodynamic flocking models in the limit of large attraction-repulsion interactions
Thierry Goudon, Antoine Mellet
We study the collective dynamics of a population of particles/organisms subject to self-consistent attraction-repulsion interactions and an external velocity field. The starting po…
Diffusion-aggregation equations and volume-preserving mean curvature flows
Jiwoong Jang, Antoine Mellet
The Patlak-Keller-Segel system of equations (PKS) is a classical example of aggregation-diffusion equation. It describes the aggregation of some organisms via chemotaxis, limited b…
Volume-preserving mean-curvature flow as a singular limit of a diffusion-aggregation equation
Antoine Mellet, Michael Rozowski
The Patlak-Keller-Segel system of equations (PKS) is a classical example of aggregation-diffusion equation in which the repulsive effect of diffusion is in competition with the att…