Date of Original Version
This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version is available at http://dx.doi.org/10.1016/j.na.2011.08.057
Abstract or Description
We investigate some dynamical properties of nonlocal interaction equations. We consider sets of particles interacting pairwise via a potential W, as well as continuum descriptions of such systems. The typical potentials we consider are repulsive at short distances, but attractive at long distances. The main question we consider is whether an initially localized configuration remains localized for all times, regardless of the number of particles or their arrangement. In particular we find sufficient conditions on the potentialW for the above “confinement” property to hold. We use the framework of weak measure solutions developed in Carrillo et al. (2011)  to provide unified treatment of both particle and continuum systems.
Nonlinear Analysis: Theory, Methods & Applications, 75, 2, 550-558.