GENERAL DECAY OF SOLUTIONS FOR A VISCOELASTIC EQUATION WITH BALAKRISHNAN-TAYLOR DAMPING AND NONLINEAR BOUNDARY DAMPING-SOURCE INTERACTIONS

doi:10.1016/S0252-9602(15)30032-1

Abstract

Abstract:

A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions imposed on the source and the damping, we establish uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function.

Key words: Balakrishnan-Taylor damping, global existence, general decay, relaxation function, viscoelastic equation

CLC Number:

35L70

Shun-Tang WU. GENERAL DECAY OF SOLUTIONS FOR A VISCOELASTIC EQUATION WITH BALAKRISHNAN-TAYLOR DAMPING AND NONLINEAR BOUNDARY DAMPING-SOURCE INTERACTIONS[J].Acta mathematica scientia,Series B, 2015, 35(5): 981-994.

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