A class of kinetic models for chemotaxis with threshold to prevent overcrowding (Q874846)

Summary: We introduce three new examples of kinetic models for chemotaxis, where a kinetic equation for the phase-space density is coupled to a parabolic or elliptic equation for the chemo-attractant, in two or three dimensions. We prove that these models have global-in-time existence and rigorously converge in the drift-diffusion limit to the \textit{E. F. Keller} and \textit{L. A. Segel} model [Model for chemotaxis. J. Theor. Biol. 30, 225--234 (1971; Zbl 1170.92307)]. Furthermore, the cell density is uniformly-in-time bounded. This implies, in particular, that the limit model also has global existence of solutions.