Journal article
NONLINEAR STABILITY OF TRAVELING WAVES TO A HYPERBOLIC-PARABOLIC SYSTEM MODELING CHEMOTAXIS
SIAM journal on applied mathematics, Vol.70(5), pp.1522-1541
01/01/2009
DOI: 10.1137/09075161X
Abstract
We prove nonlinear stability of traveling waves of arbitrary amplitudes to a hyperbolic-parabolic system modeling repulsive chemotaxis. In contrast to the previous related results, where various smallness conditions on wave strengths were imposed, we are able to prove the nonlinear stability of the traveling waves with arbitrary amplitudes under small perturbations in spite of partial diffusion in the model. Moreover, we perform numerical experiments to verify our theoretical results. Finally, the biological implications are discussed. Our results indicate that when the dissipative effect is not negligible, the cell density distribution approaches a smooth viscous shock profile asymptotically if the chemotaxis is repulsive.
Details
- Title: Subtitle
- NONLINEAR STABILITY OF TRAVELING WAVES TO A HYPERBOLIC-PARABOLIC SYSTEM MODELING CHEMOTAXIS
- Creators
- Tong Li - Univ Iowa, Dept Math, Iowa City, IA 52242 USAZhi-An Wang - Univ Minnesota, Inst Math & Its Applicat, Minneapolis, MN 55455 USA
- Resource Type
- Journal article
- Publication Details
- SIAM journal on applied mathematics, Vol.70(5), pp.1522-1541
- Publisher
- SIAM PUBLICATIONS
- DOI
- 10.1137/09075161X
- ISSN
- 0036-1399
- eISSN
- 1095-712X
- Number of pages
- 20
- Grant note
- Institute for Mathematics and Its Applications (IMA), University of Minnesota University of Iowa
- Language
- English
- Date published
- 01/01/2009
- Academic Unit
- Mathematics
- Record Identifier
- 9984241042402771
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