Journal
PHYSICA D-NONLINEAR PHENOMENA
Volume 260, Issue -, Pages 49-64Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physd.2012.11.004
Keywords
Swarm equilibria; Biological aggregations; Newtonian potential; Global attractors
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Funding
- NSERC [PIN-315973]
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We consider the aggregation equation rho(t) - del . (rho del K (*) rho) = 0 in R-n, where the interaction potential K incorporates short-range Newtonian repulsion and long-range power-law attraction. We study the global well-posedness of solutions and investigate analytically and numerically the equilibrium solutions. We show that there exist unique equilibria supported on a ball of R-n. By using the method of moving planes we prove that such equilibria are radially symmetric and monotone in the radial coordinate. We perform asymptotic studies for the limiting cases when the exponent of the power-law attraction approaches infinity and a Newtonian singularity, respectively. Numerical simulations suggest that equilibria studied here are global attractors for the dynamics of the aggregation model. (c) 2012 Elsevier B.V. All rights reserved.
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