Nonlinear stability of traveling waves to a hyperbolic-parabolic system modeling chemotaxis

Tong Li, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

75 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)1522-1541
Number of pages20
JournalSIAM Journal on Applied Mathematics
Volume70
Issue number5
DOIs
Publication statusPublished - 1 Dec 2009
Externally publishedYes

Keywords

  • Chemotaxis
  • Energy estimates
  • Hyperbolic-parabolic system
  • Large amplitudes
  • Nonlinear stability
  • Viscous shock waves

ASJC Scopus subject areas

  • Applied Mathematics

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