Stability of stationary states of non-local equations with singular interaction potentials
Type
ArticleAuthors
Fellner, KlemensRaoul, Gaël
Date
2011-04Permanent link to this record
http://hdl.handle.net/10754/599711
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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.Citation
Fellner K, Raoul G (2011) Stability of stationary states of non-local equations with singular interaction potentials. Mathematical and Computer Modelling 53: 1436–1450. Available: http://dx.doi.org/10.1016/j.mcm.2010.03.021.Sponsors
Both authors would like to thank Prof. Jose A. Carrillo, Dr. Marco Di Francesco and Prof. Christian Schmeiser for many valuable discussions. KF has been supported by Award No. KUK-I1-007-43 of Peter A. Markowich, made by King Abdullah University of Science and Technology (KAUST) and by the bilateral Austria-France project (Austria: FR 05/2007, France: Amadeus 13785 UA). GR has partially been supported by the DEASE program affiliated at the WPI, Wolfgang Pauli Institute, University of Vienna, and by the ANR grant CBDif.Publisher
Elsevier BVae974a485f413a2113503eed53cd6c53
10.1016/j.mcm.2010.03.021