General decay rate for weak viscoelastic wave equation with Balakrishnan-Taylor damping and time-varying delay

A weak viscoelastic wave equation with Balakrishnan-Taylor damping and internal time-varying delay in a bounded domain is considered. The Balakrishnan-Taylor damping appears in the flutter panel equation and the spillover problem which was initially proposed by Balakrishnan and Taylor in 1989. The presence of delay may be a source of instability. Under appropriate assumptions on the source term, with the relaxation function and certain initial data and by adopting the perturbed energy method, we establish general decay estimate for the energy, which depends on the behavior of the relation function, and which is not necessarily decaying in a polynomial or exponential fashion.. (C) 2019 Elsevier Ltd. All rights reserved.