Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774508 | Journal of Mathematical Analysis and Applications | 2017 | 30 Pages |
Abstract
This paper deals with the parabolic-elliptic-elliptic attraction-repulsion chemotaxis system with logistic source{ut=ââ
(D(u)âu)âââ
(Ïuâv)+ââ
(ξuâw)+ruâμu2,xâΩ,t>0,0=Îv+αuâβv,xâΩ,t>0,0=Îw+γuâδw,xâΩ,t>0, under no-flux boundary conditions in bounded domain with smooth boundary, where Ï,ξ,α,β,γ,δ,r and μ are assumed to be positive. When ΩâR3, D(u) is assumed to satisfy D(0)>0,D(u)â¥cDumâ1withmâ¥1andcD>0, it is proved that if Ïαâξγ>0 and μ=13(Ïαâξγ), then for any given u0âW1,â(Ω), the system possesses a global and bounded classical solution. For the case where D(u)â¡1 and nâ¥3, the convergence rate of the solution is established. When the random motion of the chemotactic species is neglected i.e. (D(u)â¡0) and ΩâRn(nâ¥2) is a convex domain, boundedness and the finite time blow up of the solution are investigated.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jie Zhao, Chunlai Mu, Deqin Zhou, Ke Lin,