In this work, we consider the quasilinear attraction–repulsion chemotaxis model with nonlinear signal production and logistic-type source. We present the global existence of classical solutions under appropriate regularity assumptions on the initial data. In addition, the asymptotic behavior of the solutions is studied, and our results generalize and improve some well-known results in the literature.
In this paper, we consider the following indirect signal generation and singular sensitivity
n
t
=
Δ
n
+
χ
∇
⋅
n
/
φ
c
∇
c
,
x
∈
Ω
,
t
>
0
,
c
t
=
Δ
c
−
c
+
w
,
x
∈
Ω
,
t
>
0
,
w
t
=
Δ
w
−
w
+
n
,
x
∈
Ω
,
t
>
0
,
in a bounded domain
Ω
⊂
R
N
N
=
2
,
3
with smooth boundary
∂
Ω
. Under the nonflux boundary conditions for
n
,
c
, and
w
, we first eliminate the singularity of
φ
c
by using the Neumann heat semigroup and then establish the global boundedness and rates of convergence for solution.
Boundedness and Asymptotic Behavior to a Chemotaxis System with Indirect Signal Generation and Singular Sensitivity
