Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4958729 | Computers & Mathematics with Applications | 2016 | 9 Pages |
Abstract
This paper deals with an attraction-repulsion chemotaxis system with logistic source {ut=ÎuâÏââ
(uâv)+ξââ
(uâw)+f(u),(x,t)âΩÃ(0,â),vt=Îvâα1v+β1u,(x,t)âΩÃ(0,â),wt=Îwâα2w+β2u,(x,t)âΩÃ(0,â), under homogeneous Neumann boundary conditions in a smooth bounded domain ΩâRn(nâ¥3) with nonnegative initial data (u0,v0,w0)âW1,â(Ω)ÃW2,â(Ω)ÃW2,â(Ω), where Ï>0, ξ>0, αi>0, βi>0(i=1,2) and f(u)â¤auâμu2 with aâ¥0 and μ>0. Based on the maximal Sobolev regularity and semigroup technique, it is proved that the system admits a unique globally bounded classical solution provided that nâ¥3, α1=α2 and there exists θ0>0 such that Ïβ1+ξβ2μ<θ0. The main aim of this paper is to solve the higher-dimensional boundedness question addressed by Xie and Xiang in [IMA J. Appl. Math. 81 (2016) 165-198].
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Pan Zheng, Chunlai Mu, Xuegang Hu,