期刊
MATHEMATICAL AND COMPUTER MODELLING
卷 53, 期 7-8, 页码 1436-1450出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.mcm.2010.03.021
关键词
Non-local evolution equation; Singular interaction potential; Stability analysis; Numerical simulation
类别
资金
- King Abdullah University of Science and Technology (KAUST)
- bilateral Austria-France project [FR 05/2007, Amadeus 13785 UA]
- WPI
- Wolfgang Pauli Institute, University of Vienna
- ANR
We study the large-time behaviour of a non-local evolution equation for the density of particles or individuals subject to an external and an interaction potential. In particular, we consider interaction potentials which are singular in the sense that their first derivative is discontinuous at the origin. For locally attractive singular interaction potentials we prove under a linear stability condition local non-linear stability of stationary states consisting of a finite sum of Dirac masses. For singular repulsive interaction potentials we show the stability of stationary states of uniformly bounded solutions under a convexity condition. Finally, we present numerical simulations to illustrate our results. (C) 2010 Elsevier Ltd. All rights reserved.
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