Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4958690 | Computers & Mathematics with Applications | 2016 | 16 Pages |
Abstract
This paper is concerned with a class of quasilinear chemotaxis systems generalizing the prototype (0.1){ut=Îumâââ
(uâv)+μuâur,xâΩ,t>0,vt=Îvâv+u,xâΩ,t>0,âuâν=âvâν=0,xââΩ,t>0,u(x,0)=u0(x),v(x,0)=v0(x)xâΩ, in a smooth bounded domain ΩâRN(Nâ¥2) with parameters m,râ¥1 and μâ¥0. The PDE system in (0.1) is used in mathematical biology to model the mechanism of chemotaxis, that is, the movement of cells in response to the presence of a chemical signal substance which is in homogeneously distributed in space. It is shown that if m{>2â2Nif11+(N+2â2r)+N+2ifN+22â¥râ¥N+2N,â¥1ifr>N+22, and the nonnegative initial data (u0,v0)âCι(ΩÌ)ÃW1,â(Ω)(ι>0), then (0.1) possesses at least one global bounded weak solution. Apart from this, it is proved that if μ=0 then both u(â
,t) and v(â
,t) decay to zero with respect to the norm in Lâ(Ω) as tââ.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Jiashan Zheng, Yifu Wang,