Global dynamics and diffusion limit of a one-dimensional repulsive chemotaxis model

Zhian Wang, Kun Zhao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

22 Citations (Scopus)

Abstract

In the first part of this paper, we investigate the qualitative behavior of classical solutions for a one-dimensional parabolic system derived from a repulsive chemotaxis model on bounded domains. It is shown that classical solutions to the initial-boundary value problem exist globally in time for large data and converge to constant equilibrium states exponentially in time. The results indicate that repulsive chemotaxis exhibits a strong tendency against pattern formation. In the second part, we study diffusion limit and convergence rate of the model toward a non-diffusive problem studied in [11]. It is shown that when the chemical diffusion coefficient ∈ tends to zero, the solution is convergent in L∞-norm with respect to ∈ at order O(∈).
Original languageEnglish
Pages (from-to)3027-3046
Number of pages20
JournalCommunications on Pure and Applied Analysis
Volume12
Issue number6
DOIs
Publication statusPublished - 1 Nov 2013

Keywords

  • Chemotaxis
  • Classical solution
  • Convergence rate
  • Diffusion limit
  • Global well-posedness
  • Initial-boundary value problem
  • Long-time behavior

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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