NONLINEAR STABILITY OF LARGE AMPLITUDE VISCOUS SHOCK WAVES OF A GENERALIZED HYPERBOLIC-PARABOLIC SYSTEM ARISING IN CHEMOTAXIS

Tong Li; Zhi-An Wang

doi:10.1142/S0218202510004830

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NONLINEAR STABILITY OF LARGE AMPLITUDE VISCOUS SHOCK WAVES OF A GENERALIZED HYPERBOLIC-PARABOLIC SYSTEM ARISING IN CHEMOTAXIS

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NONLINEAR STABILITY OF LARGE AMPLITUDE VISCOUS SHOCK WAVES OF A GENERALIZED HYPERBOLIC-PARABOLIC SYSTEM ARISING IN CHEMOTAXIS

Tong Li and Zhi-An Wang

Mathematical models & methods in applied sciences, Vol.20(11), pp.1967-1998

11/01/2010

DOI: 10.1142/S0218202510004830

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Abstract

Traveling wave (band) behavior driven by chemotaxis was observed experimentally by Adler(1,2) and was modeled by Keller and Segel.15 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. The numerical simulations are performed to show the stability of the traveling waves under various perturbations.

Mathematics

Mathematics, Applied

Physical Sciences

Science & Technology

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Title: Subtitle: NONLINEAR STABILITY OF LARGE AMPLITUDE VISCOUS SHOCK WAVES OF A GENERALIZED HYPERBOLIC-PARABOLIC SYSTEM ARISING IN CHEMOTAXIS
Creators: Tong Li - University of Iowa
Zhi-An Wang - Hong Kong Polytechnic University
Resource Type: Journal article
Publication Details: Mathematical models & methods in applied sciences, Vol.20(11), pp.1967-1998
Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202510004830
ISSN: 0218-2025
eISSN: 1793-6314
Number of pages: 32
Grant note: Hong Kong Polytechnic University
Language: English
Date published: 11/01/2010
Academic Unit: Mathematics
Record Identifier: 9984241046202771

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