Asymptotic Analysis of a Chemotaxis System with Non-Diffusive Memory

Angela Stevens and Juan J.L. Velazquez

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Submission date: 05. Apr. 2012
Pages: 75
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Abstract:
In this paper detailed long time asymptotics are calculated for a chemotaxis equation with a logarithmic chemotactic sensitivity which is coupled to an ODE. We consider the radial symmetric setting in any space dimension. The ODE describes a non-diffusing chemical, which is produced by the chemotactic species itself. Intuitively this model can be related to self-attracting reinforced random walks for many particles. Thus the behavior crucially differs with respect to existence of global solutions and the occurrence of finite or infinite time blow-up if compared to the classical Keller-Segel model. Blow-up is more likely to happen in lower dimensions in the present case. This PDE-ODE system is, among others, used in the literature to model haptotaxis and angiogenesis.