Stability of stationary states of non-local equations with singular interaction potentials

Klemens Fellner, Gaël Raoul

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

Abstract

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. © 2010 Elsevier Ltd.
Original languageEnglish (US)
Pages (from-to)1436-1450
Number of pages15
JournalMathematical and Computer Modelling
Volume53
Issue number7-8
DOIs
StatePublished - Apr 2011
Externally publishedYes

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