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Aggregation-diffusion equations: dynamics, asymptotics, and singular limits
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 …
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
We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear
nonlocal equations with a gradient flow structure. These properties allow for accurate …
nonlocal equations with a gradient flow structure. These properties allow for accurate …
Primal dual methods for Wasserstein gradient flows
Combining the classical theory of optimal transport with modern operator splitting
techniques, we develop a new numerical method for nonlinear, nonlocal partial differential …
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
We discuss several continuum cell-cell adhesion models based on the underlying
microscopic assumptions. We propose an improvement on these models leading to sharp …
microscopic assumptions. We propose an improvement on these models leading to sharp …
Zoology of a nonlocal cross-diffusion model for two species
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 …
positivity preserving finite volume scheme based on the numerical method introduced in [JA …
Local and global existence for nonlocal multispecies advection-diffusion models
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 …
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
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 …
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
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 …
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
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 …
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 …
coefficients, for which the Gelfand-triple argument developed for (local) monotone SPDEs …