Liangchen Wang, Shahab Ud-Din Khan, Salah Ud-Din Khan
Abstract:
In this article, we consider a chemotaxis system with consumption
of chemoattractant and logistic source
under homogeneous Neumann boundary conditions in a smooth bounded domain
, with non-negative initial data
and
satisfying
(for some
).
is a parameter referred to as
chemosensitivity and
is assumed to generalize the logistic function
It is proved that if
is sufficiently small
then the corresponding initial-boundary value problem possesses a unique
global classical solution that is uniformly bounded.
Submitted July 1, 2013. Published September 19, 2013.
Math Subject Classifications: 35B35, 35K55, 92C17.
Key Words: Chemotaxis; global existence; boundedness; logistic source.
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Liangchen Wang College of Mathematics and Statistics Chongqing University, Chongqing 401331, China email: liangchenwang324@126.com | |
Shahab Ud-Din Khan College of Mathematics and Statistics Chongqing University, Chongqing 401331, China email: sudkhan@163.com | |
Salah Ud-Din Khan College of Engineering, King Saud University P.O. Box 800, Riyadh 11421, Kingdom of Saudi Arabia email: salahudkhan@126.com |
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