Geodesic
Boundedness in a chemotaxis system with consumption of chemoattractant and logistic source
Electronic Journal of Differential Equations, Tome 2013 (2013).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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__a38,
     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},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a38/}
}
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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__a38/