ABSTRACT
This paper deals with the initial-boundary value problem for the two-species chemotaxis-competition system with two signals
under the homogeneous Neumann boundary condition, where
,
,
,
,
,
, and
is a smooth bounded domain. If
,
,
and
are sufficiently small, then the system possesses a globally bounded classical solution for any suitably regular initial data
. Furthermore, by constructing some appropriate functionals, it is shown that
For the weak competition case, if
are sufficiently large, then the solution
converges to
exponentially as
.
For the strong-weak competition case, if
is sufficiently large, then the solution
converges to
with exponential decay when
, and with algebraic decay when
.
Acknowledgments
This work is supported in part by the Fundamental Research Funds for the Central Universities under grant XDJK2020C054, 106112016CDJXZ238826 and 2019CDJCYJ001, NSFC under grants 11771062 and 11971082, the Postdoctoral Program for Innovative Talent Support of Chongqing, Chongqing Key Laboratory of Analytic Mathematics and Applications.
Disclosure statement
No potential conflict of interest was reported by the author(s).