Abstract
This paper deals with the following attraction–repulsion chemotaxis system with logistic source
under homogeneous Neumann boundary conditions in a bounded domain
with smooth boundary, where
are assumed to be positive constants and
with
and
. It is shown that the system admits a unique globally bounded classical solution provided that space dimension n = 2, or
and
, or
and
with some
. Furthermore, under the additional assumption μ is suitably large, we show that the global classical solution will converge to the constant steady state
exponentially as
. Our results imply that the logistic source plays an important role on the behavior of the solutions in this model.
Acknowledgments
The paper is supported by the National Science Foundation of China(11301419) and the Meritocracy Research Funds of China West Normal University [17YC382].
Disclosure statement
No potential conflict of interest was reported by the author(s).