The Patlak-Keller-Segel model and its variations: properties of solutions via maximum principle
The qualitative and asymptotic behavior of radially stationary solutions for a class of diffusion-aggregation equations is investigated. A universal estimate for compactly supported weak solutions is established. The challenge in the analysis consists of the nonlocal aggregation term as well as the degeneracy of the diffusion term, which generates compactly supported solutions. The key tools of the investigation of the considered problem are maximum-principle type arguments as well as estimates on mass concentration of solutions.
scientific article; zbMATH DE number 6070861