An Aggregation Equation with Degenerate Diffusion: Qualitative Property of Solutions

@article{Chayes2013AnAE,
  title={An Aggregation Equation with Degenerate Diffusion: Qualitative Property of Solutions},
  author={L. Chayes and Inwon Kim and Yao Yao},
  journal={SIAM J. Math. Anal.},
  year={2013},
  volume={45},
  pages={2995-3018}
}
We study a nonlocal aggregation equation with degenerate diffusion, set in a periodic domain. This equation represents the generalization to $m > 1$ of the McKean--Vlasov equation, where here the “diffusive” portion of the dynamics are governed by porous medium self-interactions. We focus primarily on $m\in(1,2]$ with particular emphasis on $m = 2$. In general, we establish regularity properties and, for small interaction, exponential decay to the uniform stationary solution. For $m=2$, we… Expand
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