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

@article{Fellner2011StabilityOS,
  title={Stability of stationary states of non-local equations with singular interaction potentials},
  author={Klemens Fellner and Ga{\"e}l Raoul},
  journal={Mathematical and Computer Modelling},
  year={2011},
  volume={53},
  pages={1436-1450}
}
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 sums of Dirac masses… CONTINUE READING
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