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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.
Global existence of classical solutions for a hyperbolic chemotaxis model and its parabolic limit
Hyung Ju Hwang, Kyungkeun Kang and Angela StevensAbstract
We consider a one dimensional hyperbolic system for chemosensitive movement, especially for chemotactic behavior. The model consists of two hyperbolic differential equations for the chemotactic species and is coupled with either a parabolic or an elliptic equation for the dynamics of the external chemical signal. The speed of the chemotactic species is allowed to depend on the external signal and the turning rates may depend on the signal and its gradients in space and time, as observed in experiments. Global classical solutions are established for regular initial data and a parabolic limit is proved.
- Received:
- 10.04.03
- Published:
- 10.04.03
- MSC Codes:
- 35L60, 35M10, 58J45, 92C17
- Keywords:
- chemotaxis, hyperbolic model, global existence, parabolic limit