Numerical and Analytical Investigation of Chemotaxis Models

The Keller-Segel system is a linear parabolic-elliptic system, which describes the aggregation of slime molds resulting from their chemotactic features. By chemotaxis we understand the movement of an organism (like bacteria) in response to chemical stimulus, for example attraction by certain chemicals in the environment. In this paper, we use the results of a paper by Zhou and Saito to validate our finite volume method with respect to blow-up analysis and equilibrium solutions. Based on these results, we study model variations and their blow-up behavior numerically. We will discuss the question whether or not conservative numerical methods are able to model a blow-up behavior in the case of non-global existence of solutions.