PDE Models for Chemotactic Movements: Parabolic, Hyperbolic and Kinetic

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Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ2 (2007, methodology): “For further bibliography on the Patlak-Keller-Segel system and related models we refer the interested reader to the surveys [28, 29, 45 ].”
On the global existence of solutions to an aggregation model (2008, background): “In the literature there are two main classes of models that describe the phenomenon of vasculogenesis: one considers the movement of endothelial cells due to chemotaxis, where a chemical gradient can direct cell migration both up and down a concentration gradient (see [3,4,5]), and the second one re”
Global Existence for a Kinetic Model of Chemotaxis via Dispersion and Strichartz Estimates (2007, methodology): “The proof starts with the fact that the L1x v-norm of the solution f is a-priori bounded thanks to conservation of mass ∫∫ V f t x v dv dx = ∫∫ V f0 x v dv dx= M (1.2) and then proceeds to bootstrap higher Lpx v-norms based on strong dispersion estimates (see Glassey, 1996; Perthame, 2004a).”