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MiS Preprint
20/2012

Asymptotic Analysis of a Chemotaxis System with Non-Diffusive Memory

Angela Stevens and Juan J.L. Velazquez

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.

Received:
Apr 5, 2012
Published:
Apr 19, 2012

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Preprint
2012 Repository Open Access
Angela Stevens and Juan J. L. Velázquez

Asymptotic analysis of a chemotaxis system with non-diffusive memory