Asymptotic stability of a viscoelastic problem with Balakrishnan–Taylor damping and time-varying delay. (15th September 2017)

• Record Type: Journal Article
• Authors: Kang, Jum-Ran; Lee, Mi Jin; Park, Sun Hye
• Is Part Of: Computers & mathematics with applications. Volume 74:issue 6(2017)
• Page Start: 1506
• Page End: 1515
• Publication Date: 2017-09-15
• Subjects: Balakrishnan–Taylor damping -- General decay rate -- Time-varying delay -- Convex function; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.06.033
• Languages: English
• ISSNs: 0898-1221

Abstract

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.