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- W2963949813 abstract "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 solutions with subcritical mass converge to a self-similar dissipating solution algebraically fast. For non-radial solutions, we obtain convergence towards the self-similar dissipating solution when the mass is sufficiently small. We also apply the mass comparison method to another aggregation model with repulsive-attractive interaction, and prove that radial solutions converge to the stationary solution exponentially fast." @default.
- W2963949813 created "2019-07-30" @default.
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- W2963949813 date "2014-02-01" @default.
- W2963949813 modified "2023-09-26" @default.
- W2963949813 title "Asymptotic behavior for critical Patlak–Keller–Segel model and a repulsive–attractive aggregation equation" @default.
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- W2963949813 doi "https://doi.org/10.1016/j.anihpc.2013.02.002" @default.
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