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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.
A chemotaxis--model for directed tissue growth
Hartmut SchwetlickAbstract
In this paper we propose a chemotaxis--growth--system for the modelling of stimulated tissue growth. Such phenomena frequently arise in wound healing and angiogenesis and used to be modeled by reaction-diffusion alone. The model focuses on the role of the epidermal growth factor in increasing mitotic activity but also serving as an chemo-attractant for the migrating cells. We show that travelling wave solutions exist, having a uniquely determined minimal wave speed depending on the diffusivity and the sensitivity of the chemotactic population. In particular, the speed is enhanced for stronger chemotactic sensitivity proposing a mechanism to increase healing rates compared to the model with purely diffusion driven migration.
- Received:
- 09.03.05
- Published:
- 09.03.05