In this talk, I will present some recent results on the longtime behavior of global solutions to initial-boundary value problems of the quasilinear Keller-Segel system. We consider this system with non-degenerate as well as degenerate diffusions. For the former case, with the help of a non-smooth version of Lojasiewicz-Simon inequality, we prove that any globally bounded classical solution will converge to an equilibrium as time goes to infinity. If the diffusion is degenerate, we consider the typical porous medium case. We establish global existence of weak solutions. In addition, asymptotic behavior was studied via Lojasiewicz-Simon approach.

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