Asymptotic stability of a viscoelastic problem with Balakrishnan–Taylor damping and time-varying delay. (15th September 2017) - Kang, Jum-Ran; Lee, Mi Jin; Park, Sun Hye
Abstract: A viscoelastic problem with Balakrishnan–Taylordamping and time-varying delay of the form u t t − ( a + b ‖ ∇ u ‖ 2 + σ ( ∇ u, ∇ u t ) ) Δ u + ∫ 0 t g ( t − s ) Δ u ( s ) d s + μ 1 f 1 ( u t ( x, t ) ) + μ 2 f 2 ( u t ( x, t − τ ( t ) ) ) = 0 is considered. We prove a general stability result for the equation without the condition μ 2 > 0 by establishing some Lyapunov functionals which are equivalent to the energy of the equation instead of multiplier technique and using some properties of convex functions.