Asymptotic dynamics of the one-dimensional attraction-repulsion Keller-Segel model

Hai Yang Jin, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

46 Citations (Scopus)

Abstract

The asymptotic behavior of the attraction-repulsion Keller-Segel model in one dimension is studied in this paper. The global existence of classical solutions and nonconstant stationary solutions of the attraction-repulsion Keller-Segel model in one dimension were previously established by Liu and Wang (2012), which, however, only provided a time-dependent bound for solutions. In this paper, we improve the results of Liu and Wang (2012) by deriving a uniform-in-time bound for solutions and furthermore prove that the model possesses a global attractor. For a special case where the attractive and repulsive chemical signals have the same degradation rate, we show that the solution converges to a stationary solution algebraically as time tends to infinity if the attraction dominates.
Original languageEnglish
Pages (from-to)444-457
Number of pages14
JournalMathematical Methods in the Applied Sciences
Volume38
Issue number3
DOIs
Publication statusPublished - 1 Jan 2015

Keywords

  • Attraction-repulsion
  • Chemotaxis
  • Classical solutions
  • Global dynamics
  • Stationary solutions

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this