Author:
Gheraibia Billel,Boumaza Nouri
Abstract
AbstractIn this paper, we study the initial boundary value problem for the following viscoelastic wave equation with Balakrishnan–Taylor damping and a delay term where the relaxation function satisfies $g'(t)\leq -\xi (t)g^{r}(t)$
g
′
(
t
)
≤
−
ξ
(
t
)
g
r
(
t
)
, $t\geq 0$
t
≥
0
, $1\leq r< \frac{3}{2}$
1
≤
r
<
3
2
. The main goal of this work is to study the global existence, general decay, and blow-up result. The global existence has been obtained by potential-well theory, the decay of solutions of energy has been established by introducing suitable energy and Lyapunov functionals, and a blow-up result has been obtained with negative initial energy.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
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