# Asymptotic Behavior for Critical Patlak-Keller-Segel model and an Repulsive-Attractive Aggregation Equation

@article{Yao2011AsymptoticBF, title={Asymptotic Behavior for Critical Patlak-Keller-Segel model and an Repulsive-Attractive Aggregation Equation}, author={Yao Yao}, journal={arXiv: Analysis of PDEs}, year={2011} }

In this paper we study the long time asymptotic behavior for a class of diffusion-aggregation equations. Most results except the ones in Section 3.3 concern radial solutions. The main tools used in the paper are maximum-principle type arguments on mass concentration of solutions, as well as energy method. For the Patlak-Keller-Segel problem with critical power $m=2-2/d$, we prove that all radial solutions with critical mass would converge to a family of stationary solutions, while all radial… Expand

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