General Decay of a Nonlinear Viscoelastic Wave Equation with Balakrishnân-Taylor Damping and a Delay Involving Variable Exponents. (11th May 2022)

• Record Type: Journal Article
• Authors: Zuo, Jiabin; Rahmoune, Abita; Li, Yanjiao
• Other Names: Meskhi Alexander Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-05-11
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/9801331
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : This paper was aimed at investigating the stability of the following viscoelastic problem with Balakrishnân-Taylor damping and variable-exponent nonlinear time delay term u t t − M ∇ u 2 2 Δ u + α t ∫ 0 t g t − s Δ u s d s + μ 1 u t p . − 2 u t + μ 2 u t t − τ p . − 2 u t t − τ = 0 in Ω × ℝ +, where Ω is a bounded domain of ℝ n, p . : Ω ¯ ⟶ ℝ is a measurable function, g > 0 is a memory kernel that decays exponentially, α ≥ 0 is the potential, and M ∇ u 2 2 = a + b ∇ u t 2 2 + σ ∫ Ω ∇ u ∇ u t d x for some constants a > 0, b ≥ 0, and σ > 0 . Under some assumptions on the relaxation function, we use some suitable Lyapunov functionals to derive the general decay estimate for the energy. The problem considered is novel and meaningful because of the presence of the flutter panel equation and the spillover problem including memory and variable-exponent time delay control. Our result generalizes and improves previous conclusion in the literature.