TY - JOUR
T1 - Asymptotic Behavior for a Viscoelastic Wave Equation with a Time-varying Delay Term
AU - Wu , Shun Tang
JO - Journal of Partial Differential Equations
VL - 1
SP - 22
EP - 35
PY - 2016
DA - 2016/03
SN - 29
DO - http://doi.org/10.4208/jpde.v29.n1.3
UR - https://global-sci.org/intro/article_detail/jpde/5076.html
KW - Global existence
KW - asymptotic behavior
KW - general decay
KW - time-varying delay
AB -  The following viscoelastic wave equation with a time-varying delay term in internal feedback $|u_t|^ρu_{tt}-Δu-Δu_{tt}+∫^t_0g(t-s)Δu(s)ds+μ_1u_t(x,t)+μ_2u_t(x,t-τ(t))=0$, is considered in a bounded domain. Under appropriate conditions on μ_1, μ_2 and on the kernel g, we establish the general decay result for the energy by suitable Lyapunov functionals.