Porous medium equation and cross-diffusion systems as limit of nonlocal interaction

Exponential Convergence to Equilibrium for Coupled Systems of Nonlinear Degenerate Drift Diffusion Equations

(2023) Lisa Beck et al.   SIAM JOURNAL ON MATHEMATICAL ANALYSIS

Deterministic particle approximation of aggregation-diffusion equations on unbounded domains

(2022) Sara Daneri et al.   JOURNAL OF DIFFERENTIAL EQUATIONS

Many-particle limit for a system of interaction equations driven by Newtonian potentials

(2021) Marco Di Francesco et al.   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Rigorous Derivation of Population Cross-Diffusion Systems from Moderately Interacting Particle Systems

(2021) Li Chen et al.   JOURNAL OF NONLINEAR SCIENCE

From Nonlocal to Classical Shigesada--Kawasaki--Teramoto Systems: Triangular Case with Bounded Coefficients

(2020) Ayman Moussa   SIAM JOURNAL ON MATHEMATICAL ANALYSIS

A blob method for diffusion

(2019) José Antonio Carrillo et al.   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Rigorous mean-field limit and cross-diffusion

(2019) Li Chen et al.   ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK

Nonlinear degenerate cross-diffusion systems with nonlocal interaction

(2018) M. Di Francesco et al.   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts

(2017) Guillaume Carlier et al.   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Transport distances and geodesic convexity for systems of degenerate diffusion equations

(2015) Jonathan Zinsl et al.   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

A blob method for the aggregation equation

(2015) Katy Craig et al.   MATHEMATICS OF COMPUTATION

Non local Lotka-Volterra system with cross-diffusion in an heterogeneous medium

(2014) Joaquin Fontbona et al.   JOURNAL OF MATHEMATICAL BIOLOGY

Curves of steepest descent are entropy solutions for a class of degenerate convection–diffusion equations

(2013) Marco Di Francesco et al.   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Measure solutions for non-local interaction PDEs with two species

(2013) Marco Di Francesco et al.   NONLINEARITY

Gamma-convergence of gradient flows on Hilbert and metric spaces and applications

(2011) Sylvia Serfaty   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations

(2011) J. A. Carrillo et al.   DUKE MATHEMATICAL JOURNAL

Lp theory for the multidimensional aggregation equation

(2010) Andrea L. Bertozzi et al.   COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

A Family of Nonlinear Fourth Order Equations of Gradient Flow Type

(2009) Daniel Matthes et al.   COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

Eulerian Calculus for the Displacement Convexity in the Wasserstein Distance

(2008) Sara Daneri et al.   SIAM JOURNAL ON MATHEMATICAL ANALYSIS