Asymptotic Behavior for a Viscoelastic Wave Equation with a Time-varying Delay Term

Abstract

" The following viscoelastic wave equation with a time-varying delay term in internal feedback $|u_t|^\u03c1u_{tt}-\u0394u-\u0394u_{tt}+\u222b^t_0g(t-s)\u0394u(s)ds+\u03bc_1u_t(x,t)+\u03bc_2u_t(x,t-\u03c4(t))=0$, is considered in a bounded domain. Under appropriate conditions on \u03bc_1, \u03bc_2 and on the kernel g, we establish the general decay result for the energy by suitable Lyapunov functionals."