Swarm Dynamics and Equilibria for a Nonlocal Aggregation Model

Razvan Fetecau
Simon Fraser University

We consider an aggregation equation given by the continuity equation, where velocity is given in terms of density via a convolution with an interaction potential. The latter models short-range repulsion and long-range attraction. We study a family of interaction potentials with repulsion given by a Newtonian potential and attraction in the form of a power law. We show global well-posedness of solutions and investigate analytically and numerically the equilibria and their global stability. The equilibria have biologically relevant features, such as finite densities and compact support with sharp boundaries. This is joint work with Yanghong Huang and Theodore Kolokolnikov.

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