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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Issue 3 (September 2021)   > Article

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

Déficience D’une Onde Viscoélastique Non Linéaire : Équation Avec Dissipation Aux Limites


Amel Boudiaf
University of setif
Algeria

Salah Drabla
University of setif
Algeria



Published on 6 September 2021   DOI : 10.21494/ISTE.OP.2021.0723

Abstract

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In this work we establish a general decay rate for a nonlinear viscoelastic wave equation with boundary dissipation where the relaxation function satisfies $$$g^{\prime }\left( t\right) \leq -\xi \left( t\right) g^{p} % \left( t\right) , t\geq 0, 1\leq p\leq \frac{3}{2}.$$$ This work generalizes and improves earlier results in the literature.

In this work we establish a general decay rate for a nonlinear viscoelastic wave equation with boundary dissipation where the relaxation function satisfies $$$g^{\prime }\left( t\right) \leq -\xi \left( t\right) g^{p} % \left( t\right) , t\geq 0, 1\leq p\leq \frac{3}{2}.$$$ This work generalizes and improves earlier results in the literature.

Viscoelastic General decay Relaxation function Dissipation Wave equation

Viscoelastic General decay Relaxation function Dissipation Wave equation