ABSTRACT
This paper deals with the parabolic–elliptic chemotaxis-growth system with nonlinear secretion
under homogeneous Neumann boundary conditions in a bounded domain
with smooth boundary, where
, a>0, b>0, r>1,
and
is a smooth function satisfying
with some
and
. It is shown, either
or
or
then the system admits a unique global bounded classical solution. Moreover, we obtain the large time behavior of the solution for a specific logistic source. Finally, for the case
and r=k+1, large time behavior and convergence rate are established.
Acknowledgments
The authors are very grateful to the anonymous reviewers for their careful reading and valuable comments which greatly improved this work.
Disclosure statement
No potential conflict of interest was reported by the authors.