Geodesic
Boundedness in a chemotaxis system with consumption of chemoattractant and logistic source
Electronic journal of differential equations, Tome 2013 (2013)
In this article, we consider a chemotaxis system with consumption of chemoattractant and logistic source

$\displaylines{ u_t=\Delta u-\chi\nabla\cdot(u\nabla v)+f(u),\quad x\in \Omega,\; t>0,\cr v_t=\Delta v-uv,\quad x\in\Omega,\; t>0, }$

under homogeneous Neumann boundary conditions in a smooth bounded domain

$ f(s)=as-bs^2,\quad s\geq0,\hbox{ with } a>0,\;b>0. $

It is proved that if $\|v_0\|_{L^\infty(\Omega)}>0$ is sufficiently small then the corresponding initial-boundary value problem possesses a unique global classical solution that is uniformly bounded.
Classification : 35B35, 35K55, 92C17
Keywords: chemotaxis, global existence, boundedness, logistic source 
@article{EJDE_2013__2013__a138,
     author = {Wang,  Liangchen and Khan,  Shahab Ud-Din and Khan,  Salah Ud-Din},
     title = {Boundedness in a chemotaxis system with consumption of chemoattractant and logistic source},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1295.35255},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a138/}
}
TY  - JOUR
AU  - Wang,  Liangchen
AU  - Khan,  Shahab Ud-Din
AU  - Khan,  Salah Ud-Din
TI  - Boundedness in a chemotaxis system with consumption of chemoattractant and logistic source
JO  - Electronic journal of differential equations
PY  - 2013
VL  - 2013
UR  - http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a138/
LA  - en
ID  - EJDE_2013__2013__a138
ER  - 
%0 Journal Article
%A Wang,  Liangchen
%A Khan,  Shahab Ud-Din
%A Khan,  Salah Ud-Din
%T Boundedness in a chemotaxis system with consumption of chemoattractant and logistic source
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a138/
%G en
%F EJDE_2013__2013__a138
Wang,  Liangchen; Khan,  Shahab Ud-Din; Khan,  Salah Ud-Din. Boundedness in a chemotaxis system with consumption of chemoattractant and logistic source. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a138/