Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (5): 1453-1471.doi: 10.1016/S0252-9602(17)30084-X

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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

Yamna BOUKHATEM1, Benyattou BENABDERRAHMANE2   

  1. 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

Abstract:

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.

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

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