Classical models for chemotaxis base on the Keller-Segel model. Hence the underlying motion process is Brownian motion and the paradox of infinite propagation speed appears. Here I present hyperbolic models for chemotaxis. Finite propagation speed is directly included into the model equations. For the model in 1-D the connection to the Keller-Segel model will be shown and first existence results will be presented. Numerical simulations show interesting behavior such as finite time blow-up or global existing patterns.

Joint work with A. Stevens

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1998-1999 Mathematics in Biology