期刊
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
卷 38, 期 3, 页码 444-457出版社
WILEY-BLACKWELL
DOI: 10.1002/mma.3080
关键词
chemotaxis; attraction-repulsion; classical solutions; stationary solutions; global dynamics
资金
- Hong Kong RGC General Research Fund [502711]
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. Copyright (c) 2014 John Wiley & Sons, Ltd.
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