DOI: 10.1515/dema-2024-0048 ISSN: 2391-4661
Absence of global solutions to wave equations with structural damping and nonlinear memory
Mokhtar Kirane, Abderrazak Nabti, Lotfi Jlali Abstract
We prove the nonexistence of global solutions for the following wave equations with structural damping and nonlinear memory source term
u
t
t
+
(
−
Δ
)
α
2
u
+
(
−
Δ
)
β
2
u
t
=
∫
0
t
(
t
−
s
)
δ
−
1
∣
u
(
s
)
∣
p
d
s
{u}_{tt}+{\left(-\Delta )}^{\tfrac{\alpha }{2}}u+{\left(-\Delta )}^{\tfrac{\beta }{2}}{u}_{t}=\underset{0}{\overset{t}{\int }}{\left(t-s)}^{\delta -1}{| u\left(s)| }^{p}{\rm{d}}s
and
u
t
t
+
(
−
Δ
)
α
2
u
+
(
−
Δ
)
β
2
u
t
=
∫
0
t
(
t
−
s
)
δ
−
1
∣
u
s
(
s
)
∣
p
d
s
,
{u}_{tt}+{\left(-\Delta )}^{\tfrac{\alpha }{2}}u+{\left(-\Delta )}^{\tfrac{\beta }{2}}{u}_{t}=\underset{0}{\overset{t}{\int }}{\left(t-s)}^{\delta -1}{| {u}_{s}\left(s)| }^{p}{\rm{d}}s,
posed in