Equilibria of biological aggregations with nonlocal repulsive-attractive interactions

PHYSICA D-NONLINEAR PHENOMENA

卷:260

Article

Fetecau, R. C.¹  Huang, Y.¹ 

[1] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada

关键词: Swarm equilibria;    Biological aggregations;    Newtonian potential;    Global attractors;   

DOI  :  10.1016/j.physd.2012.11.004

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free