General Decay Of A Nonlinear Viscoelastic Wave: Equation With Boundary Dissipation

Boudiaf, Amel; Drabla, Salah

doi:10.21494/iste.op.2021.0723

APAM

2021

DOI: 10.21494/iste.op.2021.0723

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General Decay Of A Nonlinear Viscoelastic Wave: Equation With Boundary Dissipation

Amel Boudiaf¹,

Salah Drabla²

Abstract: In this work we establish a general decay rate for a nonlinear viscoelastic wave equation with boundary dissipation where the relaxation function satisfies2 . This work generalizes and improves earlier results in the literature.

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2023

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Initial boundary value problem for a viscoelastic wave equation with Balakrishnan–Taylor damping and a delay term: decay estimates and blow-up result

Gheraibia,

Boumaza

2023

Bound Value Probl

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In 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.

show abstract

Initial boundary value problem for a viscoelastic wave equation with Balakrishnan–Taylor damping and a delay term: decay estimates and blow-up result

Gheraibia,

Boumaza

2023

Bound Value Probl

View full text Add to dashboard Cite

show abstract

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General Decay Of A Nonlinear Viscoelastic Wave: Equation With Boundary Dissipation

Abstract: In this work we establish a general decay rate for a nonlinear viscoelastic wave equation with boundary dissipation where the relaxation function satisfies2 . This work generalizes and improves earlier results in the literature.

Cited by 1 publication

References 12 publications

Initial boundary value problem for a viscoelastic wave equation with Balakrishnan–Taylor damping and a delay term: decay estimates and blow-up result

Initial boundary value problem for a viscoelastic wave equation with Balakrishnan–Taylor damping and a delay term: decay estimates and blow-up result

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