On the regularity and stability of three-phase-lag thermoelastic plate. Issue 15 (13th October 2022)

• Record Type: Journal Article
• Authors: Liu, Zhuangyi; Quintanilla, Ramon; Wang, Yang
• Is Part Of: Applicable analysis. Volume 101:Issue 15(2022)
• Page Start: 5376
• Page End: 5385
• Publication Date: 2022-10-13
• Subjects: Three-phase-lag thermoelastic plate -- analyticity -- exponential stability; 35Q35 -- 35Q30 -- 35L65 -- 76N10; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1892079
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper we consider the following three-phase-lag thermoelastic plate: 1 ρ u ¨ = − Δ ( μ Δ u − m θ ), c ( θ ˙ + τ q θ ¨ ) = m Δ ( u ˙ + τ q u ¨ ) + Δ ( k ∗ α + τ ν ∗ θ + k τ θ θ ˙ ) . We obtain analyticity and exponential stability for the associated C 0 -semigroup when the coefficients satisfy τ ν ≥ k ∗ τ q . The analyticity of the semigroup still holds when τ ν < k ∗ τ q . However, the instability of solution was proved by the Routh–Hurwitz rule.