We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
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.
