On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher
This is a review paper on recent results for the classical Keller-Segel model of chemotaxis in two space dimensions as well as for its higher dimensions analogs (involving nonlinear diffusion) that have a critical mass. Main results include blowup of solutions above the critical mass and fine asymptotics of solutions obtained using free energy functional and related entropy functionals. Open problems are also formulated.
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