Hyperbolic models for chemotaxis in 1-D

By Thomas Hillen, A. Stevens. 2000

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Global Existence for a Parabolic Chemotaxis Model with Prevention of Overcrowding (2001, background): “The case of V u v = uχ v has been studied in great detail in the literature (see, e.g., Childress and Percus [5, 6], Jäger and Luckhaus [11], Nagai [15], Gajewsky and Zacharias [7], Senba [28], Rascle and Ziti [25], Herrero and Velazques [8, 9], Yagi [31], Othmer and Stevens [21], or Levine and Sle”
The Diffusion Limit of Transport Equations II: Chemotaxis Equations (2002, background): “This case is studied in detail in [44, 25].”
Kinetic Models for Chemotaxis and their Drift-Diffusion Limits (2004, background): “In [ 13 ] and [14] one-dimensional discrete velocity models have been treated.”
The Diffusion Limit of Transport Equations Derived from Velocity-Jump Processes (2000, background): “In Part II and in [26] it is shown that if the speed depends on the signal, then cells accumulate at the minima of the speed distribution.”