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
Reference44 articles.
1. Adams, R., Fournier, J.: Sobolev Spaces. Academic Press, New York (2003)
2. Balakrishnan, A.V., Taylor, L.W.: Distributed parameter nonlinear damping models for flight structure, Damping 89, Flight Dynamics Lab and Air Force Wright Aeronautral Labs WPAFB (1989)
3. Conference Publication;R.W. Bass,1991
4. Boudiaf, A., Drabla, S.: General decay of a nonlinear viscoelastic wave equation with boundary dissipation. Adv. Pure Appl. Math. 12(3), 20–37 (2021)
5. Boumaza, N., Gheraibia, B.: General decay and blowup of solutions for a degenerate viscoelastic equation of Kirchhoff type with source term. J. Math. Anal. Appl. 489(2), 124185 (2020)