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MiS Preprint

Asymptotic Analysis of a Chemotaxis System with Non-Diffusive Memory

Angela Stevens and Juan J.L. Velazquez


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.

Apr 5, 2012
Apr 19, 2012

Related publications

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

Asymptotic analysis of a chemotaxis system with non-diffusive memory