Loading…
On a generalized volume-filling chemotaxis system with nonlinear signal production
This paper deals with a generalized volume-filling chemotaxis system with nonlinear signal production u t = ∇ · ( φ ( u ) ∇ u ) - ∇ · ( ψ ( u ) ∇ v ) , ( x , t ) ∈ Ω × ( 0 , ∞ ) , 0 = Δ v - μ ( t ) + f ( u ) , ( x , t ) ∈ Ω × ( 0 , ∞ ) , under homogeneous Neumann boundary conditions in a smooth boun...
Saved in:
| Published in: | Monatshefte für Mathematik 2022, Vol.198 (1), p.211-231 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | This paper deals with a generalized volume-filling chemotaxis system with nonlinear signal production
u
t
=
∇
·
(
φ
(
u
)
∇
u
)
-
∇
·
(
ψ
(
u
)
∇
v
)
,
(
x
,
t
)
∈
Ω
×
(
0
,
∞
)
,
0
=
Δ
v
-
μ
(
t
)
+
f
(
u
)
,
(
x
,
t
)
∈
Ω
×
(
0
,
∞
)
,
under homogeneous Neumann boundary conditions in a smooth bounded domain
Ω
⊂
R
n
,
n
≥
1
, where
μ
(
t
)
=
1
|
Ω
|
∫
Ω
f
(
u
(
x
,
t
)
)
d
x
,
φ
(
u
)
is a nonlinear diffusion,
ψ
(
u
)
is a nonlinear sensitivity and
f
(
u
) is a nonlinear signal production function. Under suitable assumptions on the functions
φ
,
ψ
and
f
, the global existence and finite-time blow-up of solutions for the above system are studied. The results partially generalize some recent ones obtained in Winkler (Nonlinearity 31:2031–2056, 2018), Li (J Math Anal Appl 480:123376, 2019). |
|---|---|
| ISSN: | 0026-9255 1436-5081 |
| DOI: | 10.1007/s00605-022-01669-2 |