Aggregation-diffusion equations: dynamics, asymptotics, and singular limits

JA Carrillo, K Craig, Y Yao - Active Particles, Volume 2: Advances in …, 2019‏ - Springer
Given a large ensemble of interacting particles, driven by nonlocal interactions and localized
repulsion, the mean-field limit leads to a class of nonlocal, nonlinear partial differential …

A finite-volume method for nonlinear nonlocal equations with a gradient flow structure

JA Carrillo, A Chertock, Y Huang - … in Computational Physics, 2015‏ - cambridge.org
We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear
nonlocal equations with a gradient flow structure. These properties allow for accurate …

Primal dual methods for Wasserstein gradient flows

JA Carrillo, K Craig, L Wang, C Wei - Foundations of Computational …, 2022‏ - Springer
Combining the classical theory of optimal transport with modern operator splitting
techniques, we develop a new numerical method for nonlinear, nonlocal partial differential …

A population dynamics model of cell-cell adhesion incorporating population pressure and density saturation

JA Carrillo, H Murakawa, M Sato, H Togashi… - Journal of theoretical …, 2019‏ - Elsevier
We discuss several continuum cell-cell adhesion models based on the underlying
microscopic assumptions. We propose an improvement on these models leading to sharp …

Zoology of a nonlocal cross-diffusion model for two species

JA Carrillo, Y Huang, M Schmidtchen - SIAM Journal on Applied Mathematics, 2018‏ - SIAM
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 …

Local and global existence for nonlocal multispecies advection-diffusion models

V Giunta, T Hillen, M Lewis, JR Potts - SIAM Journal on Applied Dynamical …, 2022‏ - SIAM
Nonlocal advection is a key process in a range of biological systems, from cells within
individuals to the movement of whole organisms. Consequently, in recent years, there has …

A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials

Z Sun, JA Carrillo, CW Shu - Journal of Computational Physics, 2018‏ - Elsevier
We consider a class of time-dependent second order partial differential equations governed
by a decaying entropy. The solution usually corresponds to a density distribution, hence …

Fully discrete positivity-preserving and energy-dissipating schemes for aggregation-diffusion equations with a gradient flow structure

R Bailo, JA Carrillo, J Hu - arxiv preprint arxiv:1811.11502, 2018‏ - arxiv.org
We propose fully discrete, implicit-in-time finite-volume schemes for a general family of non-
linear and non-local Fokker-Planck equations with a gradient-flow structure, usually known …

[HTML][HTML] On minimizers of interaction functionals with competing attractive and repulsive potentials

R Choksi, RC Fetecau, I Topaloglu - Annales de l'Institut Henri Poincaré C …, 2015‏ - Elsevier
We consider a family of interaction functionals consisting of power-law potentials with
attractive and repulsive parts and use the concentration compactness principle to establish …

A general framework for solving singular SPDEs with applications to fluid models driven by pseudo-differential noise

H Tang, FY Wang - arxiv preprint arxiv:2208.08312, 2022‏ - arxiv.org
In this paper we focus on nonlinear SPDEs with singularities included in both drift and noise
coefficients, for which the Gelfand-triple argument developed for (local) monotone SPDEs …