GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS

doi:10.1016/S0252-9602(17)30084-X

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (5): 1453-1471.doi: 10.1016/S0252-9602(17)30084-X

GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS

Yamna BOUKHATEM¹, Benyattou BENABDERRAHMANE²

1. Laboratory of Pure and Applied Mathematics, University of Laghouat, P. O. Box37G, Laghouat 03000, Algeria;
2. Laboratory of Pure and Applied Mathematics, Mohamed Boudiaf University, M'sila 28000, Algeria

收稿日期:2016-02-22 修回日期:2016-09-08 出版日期:2017-10-25 发布日期:2017-10-25
作者简介:Yamna BOUKHATEM,E-mail:y.boukhatem2@gmail.com;Benyattou BENABDERRAHMANE,E-mail:bbenyattou@yahoo.com

GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS

Yamna BOUKHATEM¹, Benyattou BENABDERRAHMANE²

1. Laboratory of Pure and Applied Mathematics, University of Laghouat, P. O. Box37G, Laghouat 03000, Algeria;
2. Laboratory of Pure and Applied Mathematics, Mohamed Boudiaf University, M'sila 28000, Algeria

Received:2016-02-22 Revised:2016-09-08 Online:2017-10-25 Published:2017-10-25

摘要/Abstract

摘要：

A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered. Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.

关键词: acoustic boundary conditions, general decay, time-varying delay, variable coefficients, viscoelastic equation

Abstract:

Key words: acoustic boundary conditions, general decay, time-varying delay, variable coefficients, viscoelastic equation

Yamna BOUKHATEM, Benyattou BENABDERRAHMANE. GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS[J]. 数学物理学报(英文版), 2017, 37(5): 1453-1471.

Yamna BOUKHATEM, Benyattou BENABDERRAHMANE. GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS[J]. Acta mathematica scientia,Series B, 2017, 37(5): 1453-1471.

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GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS

GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS

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