

Preprint 34/2003
Global existence of classical solutions for a hyperbolic chemotaxis model and its parabolic limit
Hyung Ju Hwang, Kyungkeun Kang, and Angela Stevens
Contact the author: Please use for correspondence this email.
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
Download full preprint: PDF (285 kB), PS ziped (258 kB)
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.