Global existence of classical solutions for a hyperbolic chemotaxis model and its parabolic limit

Hyung Ju Hwang, Kyungkeun Kang, and Angela Stevens

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Submission date: 10. Apr. 2003
Pages: 22
published in: Indiana University mathematics journal, 55 (2006) 1, p. 289-316 
DOI number (of the published article): 10.1512/iumj.2006.55.2677
Bibtex
MSC-Numbers: 35L60, 35M10, 58J45, 92C17
Keywords and phrases: chemotaxis, hyperbolic model, global existence, parabolic limit
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Abstract:
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.