Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D

Gradient flows for non-smooth interaction potentials

(2014) J.A. Carrillo et al.   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Dimensionality of Local Minimizers of the Interaction Energy

(2013) D. Balagué et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

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

Finite-time blow-up of L∞-weak solutions of an aggregation equation

(2013) Andrea L. Bertozzi et al.   Communications in Mathematical Sciences

A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity

(2012) José A. Carrillo et al.   ADVANCES IN MATHEMATICS

Sticky particle dynamics with interactions

(2012) Y. Brenier et al.   JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES

Nonlocal interactions by repulsive–attractive potentials: Radial ins/stability

(2012) D. Balagué et al.   PHYSICA D-NONLINEAR PHENOMENA

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

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

Swarm dynamics and equilibria for a nonlocal aggregation model

(2011) R C Fetecau et al.   NONLINEARITY

Lp theory for the multidimensional aggregation equation

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

Stability of stationary states of non-local equations with singular interaction potentials

(2010) Klemens Fellner et al.   MATHEMATICAL AND COMPUTER MODELLING

STABLE STATIONARY STATES OF NON-LOCAL INTERACTION EQUATIONS

(2010) KLEMENS FELLNER et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

L 2 Formulation of Multidimensional Scalar Conservation Laws

(2009) Yann Brenier   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

The behavior of solutions of multidimensional aggregation equations with mildly singular interaction kernels

(2009) Andrea L. Bertozzi et al.   CHINESE ANNALS OF MATHEMATICS SERIES B

Blow-up in multidimensional aggregation equations with mildly singular interaction kernels

(2009) Andrea L Bertozzi et al.   NONLINEARITY

A Wasserstein Approach to the One-Dimensional Sticky Particle System

(2009) Luca Natile et al.   SIAM JOURNAL ON MATHEMATICAL ANALYSIS

Large time behavior of nonlocal aggregation models with nonlinear diffusion

(2008) Martin Burger et al.   Networks and Heterogeneous Media