Affiliation:
1. Faculty of Mathematics and Computer Science University of Science Ho Chi Minh City VIETNAM
2. Vietnam National University Ho Chi Minh City VIETNAM
3. Ho Chi Minh City University of Education Ho Chi Minh City VIETNAM
4. Vietnamese-German University Binh Duong Province VIETNAM
Abstract
ABSTRACT
Let d ∈ {1, 2, 3, . . .} and Ω ⊂ ℝ
d
be open bounded with Lipschitz boundary. Consider the reaction-diffusion parabolic problem
P
{
u
t
|
x
|
4
+
Δ
(
|
Δ
u
|
m
−
2
Δ
u
)
=
k
(
t
)
|
u
|
p
−
1
u
(
x
,
t
)
∈
Ω
×
(
0
,
T
)
,
u
(
x
,
t
)
=
∂
x
j
u
(
x
,
t
)
=
0
,
(
x
,
t
)
∈
∂
Ω
×
(
0
,
T
)
,
j
∈
{
1
,
…
,
d
}
,
u
(
x
,
0
)
=
u
0
(
x
)
,
x
∈
Ω
,
where T > 0, m ∈ [2, ∞), p ∈ (1, ∞) and
0
≠
u
0
∈
W
0
2
,
m
(
Ω
)
∩
L
p
+
1
(
Ω
)
$0 \ne u_0 \in W^{2,m}_0(\Omega) \cap L^{p+1}(\Omega)$
. We investigate the upper and lower bounds on the blow-up time of a weak solution to (P).