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In this paper we investigate qualitative and asymptotic behavior of solutionsfor a class of diffusion-aggregation equations. The challenge in the analysisconsists of the nonlocal aggregation term as well as the degeneracy of thediffusion term which generates compactly supported solutions. The key toolsused in the paper are maximum-principle type arguments as well as estimates onmass concentration of solutions.

The Patlak–Keller–Segel Model and Its Variations: Properties of Solutions via Maximum Principle