Nonlinear stability of large amplitude traveling waves to hyperbolic-parabolic system modeling chemotaxis. (English) Zbl 1291.35010
Li, Tatsien (ed.) et al., Hyperbolic problems. Theory, numerics and applications. Vol. 2. Proceedings of the 13th international conference on hyperbolic problems, HYP 2010, Beijing, China, June 15–19, 2010. Hackensack, NJ: World Scientific; Beijing: Higher Education Press (ISBN 978-981-4417-08-2/v.2; 978-981-4417-06-8/set). Series in Contemporary Applied Mathematics CAM 18, 519-526 (2012).
Summary: Traveling wave (band) behavior driven by chemotaxis was observed experimentally by Adler and was modeled by Keller and Segel. For a quasilinear hyperbolic-parabolic system that arises as a non-diffusive limit of the Keller-Segel model with nonlinear kinetics, we establish the existence and nonlinear stability of traveling wave solutions with large amplitudes.
For the entire collection see [Zbl 1255.35003].
For the entire collection see [Zbl 1255.35003].
MSC:
| 35B35 | Stability in context of PDEs |
| 35C07 | Traveling wave solutions |
| 92C17 | Cell movement (chemotaxis, etc.) |
