Li, Gang; Kong, Xiangyu; Liu, Wenjun General decay for a laminated beam with structural damping and memory: the case of non-equal wave speeds. (English) Zbl 1407.35132 J. Integral Equations Appl. 30, No. 1, 95-116 (2018). Summary: In previous work, A. Lo and N.-E. Tatar [Electron. J. Differ. Equ. 2015, Paper No. 129, 14 p. (2015; Zbl 1321.35231)] studied the exponential decay for a laminated beam with viscoelastic damping acting on the effective rotation angle in the case of equal-speed wave propagations. In this paper, we continue consideration of the same problem in the case of non-equal wave speeds. In this case, the main difficulty is how to estimate the non-equal speed term. To overcome this difficulty, the second-order energy method introduced in [A. Guesmia et al., ibid. 2012, Paper No. 193, 45 p. (2012; Zbl 1295.35088)] seems to be the best choice for our problem. For a wide class of relaxation functions, we establish the general decay result for the energy without any kind of internal or boundary control. Cited in 27 Documents MSC: 35L53 Initial-boundary value problems for second-order hyperbolic systems 93C20 Control/observation systems governed by partial differential equations 93D20 Asymptotic stability in control theory 35B40 Asymptotic behavior of solutions to PDEs 74K10 Rods (beams, columns, shafts, arches, rings, etc.) Keywords:general stability; laminated beam; energy method Citations:Zbl 1321.35231; Zbl 1295.35088 × Cite Format Result Cite Review PDF Full Text: DOI Euclid References: [1] F. Boulanouar and S. Drabla, General boundary stabilization result of memory-type thermoelasticity with second sound, Electr. J. Diff. Eqs. 2014 (2014). · Zbl 1304.35084 [2] X.-G. Cao, D.-Y. Liu and G.-Q. Xu, Easy test for stability of laminated beams with structural damping and boundary feedback controls, J. Dynam. Contr. 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