A stability result for a memory-type Laminated-thermoelastic system with Maxwell–Cattaneo heat conduction

References

• G. P. Nair and S. P. Pandian, “Spotlight on laminating machines,” Colourage, vol. 53, no. 10, pp. 96–112, 2006.
   Google Scholar
• R. A. Scott, “Coated and laminated fabrics,” in Chemistry of the Textile Industry, C. M. Carr, Ed. New York: Springer, 1995, pp. 210–248.
   Google Scholar
• E. Shim, “Bonding requirements in coating and laminating of textiles,” in Joining Textiles Principles Applications, I. Jones and G.K. Stylios, Eds. Cambridge: Woodhead Publication, 2013, pp. 309–351.
   Google Scholar
• S. W. Hansen and R. Spies, “Structural damping in a laminated beams due to interfacial slip,” J. Sound Vib., vol. 204, no. 2, pp. 183–202, 1997. DOI: 10.1006/jsvi.1996.0913.
   Web of Science ®Google Scholar
• J. M. Wang, G. Q. Xu and S. P. Yung, “Exponential stabilization of laminated beams with structural damping and boundary feedback controls,” SIAM J. Control Optim., vol. 44, no. 5, pp. 1575–1597, 2005. DOI: 10.1137/040610003.
   Web of Science ®Google Scholar
• 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. Dyn. Control Syst., vol. 13, no. 3, pp. 313–336, 2007. DOI: 10.1007/s10883-007-9022-8.
   Web of Science ®Google Scholar
• C. A. Raposo, O. V. Villagrán, J. E. Muñoz Rivera and M. S. Alves, “Hybrid laminated Timoshenko beam,” J. Math. Phys., vol. 58, no. 10, pp. 101512, 2017. DOI: 10.1063/1.4998945.
   Web of Science ®Google Scholar
• N. E. Tatar, “Stabilization of a laminated beam with interfacial slip by boundary controls,” Bound. Value Probl., vol. 2015, p. 169, 2015. DOI: 10.1186/s13661-015-0432-3.
   Web of Science ®Google Scholar
• G. Li, X. Kong and L. Wenjun, “General decay for a laminated beam with structural damping and memory, the case of non-equal-wave,” J. Integr. Equ. Appl., vol. 30, no. 1, pp. 95–116, 2018. DOI: 10.1216/JIE-2018-30-1-95.
   Web of Science ®Google Scholar
• M. I. Mustafa, “Laminated Timoshenko beams with viscoelastic damping,” J. Math. Anal. Appl., vol. 466, no. 1, pp. 619–641, 2018. DOI: 10.1016/j.jmaa.2018.06.016.
   Web of Science ®Google Scholar
• A. Lo and N. E. Tatar, “Uniform stability of a laminated beam with structural memory,” Qual. Theory Dyn. Syst., vol. 15, no. 2, pp. 517–540, 2016. DOI: 10.1007/s12346-015-0147-y.
   Web of Science ®Google Scholar
• B. Feng, T. F. Ma, R. N. Monteiro and C. A. Raposo, “Dynamics of Laminated Timoshenko Beams,” J. Dyn. Diff. Equ., vol. 30, no. 4, pp. 1489–1507, 2018. DOI: 10.1007/s10884-017-9604-4.
   Web of Science ®Google Scholar
• S. E. Mukiawa, T. A. Apalara and S. A. Messaoudi, “A general and optimal stability result for a laminated beam,” J. Integ. Equ. Appl., 2020.
   Web of Science ®Google Scholar
• T. A. Apalara, “On the stability of a thermoelastic laminated beam,” Acta Math. Sci., vol. 39, no. 6, pp. 1517–1518, 2019. DOI: 10.1007/s10473-019-0604-9.
   Web of Science ®Google Scholar
• J. Ignaczak and M. Ostoja-Starzewski, Thermoelasticity with Finite Wave Speeds. Oxford: Oxford University Press, 2010.
   Google Scholar
• T. A. Apalara, “Uniform stability of a laminated beam with structural damping and second sound Z. Angew,” Z. Angew. Math. Phys., vol. 68, no. 2, pp. 41–68, 2017. DOI: 10.1007/s00033-017-0784-x.
   Web of Science ®Google Scholar
• S. W. Hansen, “A model for a two-layered plate with interfacial slip. In: Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena (Vorau, 1993),” International Series of Numerical Mathematics, vol. 118, 1993, pp. 143–170.
   Google Scholar
• A. Guesmia and S. A. Messaoudi, “On the stabilization of Timoshenko systems with memory and different speeds of wave propagation,” Appl. Math. Comput., vol. 219, no. 17, pp. 9424–9437, 2013. DOI: 10.1016/j.amc.2013.03.105.
   Web of Science ®Google Scholar
• A. Lo and N. E. Tatar, “Stabilization of laminated beams with interfcial slip,” EJDE, vol. 2015, pp. 1–14, 2015.
   Google Scholar
• T. A. Apalara and S. A. Messaoudi, “An exponential stability result of a Timoshenko system with thermoelasticity with second sound and in the presence of delay,” Appl. Math. Optim., vol. 71, no. 3, pp. 449–472, 2015. DOI: 10.1007/s00245-014-9266-0.
   Web of Science ®Google Scholar
• T. A. Apalara, S. A. Messaoudi and A. A. Keddi, “On the decay rates of Timoshenko system with second sound,” Math. Methods Appl. Sci., vol. 39, no. 10, pp. 2671–2684, 2016. DOI: 10.1002/mma.3720.
   Web of Science ®Google Scholar
• M. M. Cavalcanti and A. Guesmia, “General decay rates of solutions to a nonlinear wave equation with boundary condition of memory type,” Differ. Integr. Equ., vol. 18, no. 5, pp. 583–600, 2005.
   Web of Science ®Google Scholar
• M. L. Santos, D. S. Almeidia Junior and J. E. Munôz Rivera, “The stability of number of the Timoshenko system with second sound,” J. Differ. Equ., vol. 253, no. 9, pp. 2715–2733, 2012. DOI: 10.1016/j.jde.2012.07.012.
   Web of Science ®Google Scholar
• M. M. Chen, W. J. Liu and W. C. Zhou, “Existence and general stabilization of the Timoshenko system of thermo-viscoelasticity of type III with frictional damping and delay terms,” Adv. Nonlinear Anal., vol. 7, pp. 547–569, 2018. DOI: 10.1515/anona-2016-0085.
   Web of Science ®Google Scholar
• H. D. Fernández Sare and R. Racke, “On the stability of damped Timoshenko systems: Cattaneo versus Fourier law,” Arch. Ration. Mech. Anal., vol. 194, no. 1, pp. 221–251, 2009. DOI: 10.1007/s00205-009-0220-2.
   Web of Science ®Google Scholar
• C. A. Raposo, “Exponential stability for a structure with interfacial slip and frictional damping,” Appl. Math. Lett., vol. 53, pp. 85–91, 2016. DOI: 10.1016/j.aml.2015.10.005.
   Web of Science ®Google Scholar
• M. I. Mustafa, “General decay result for nonlinear viscoelastic equations,” J. Math. Anal. Appl., vol. 457, no. 1, pp. 134–152, 2018. DOI: 10.1016/j.jmaa.2017.08.019.
   Web of Science ®Google Scholar
• J. H. Hassan, S. A. Messaoudi and M. Zahri, “Existence and new general decay result for a viscoleastic-type Timoshenko system,” Z. Anal. Anwend., vol. 39, no. 2, pp. 185–222, 2020. DOI: 10.4171/ZAA/1657.
   Web of Science ®Google Scholar
• V. I. Arnorld, Mathematical Methods of Classical Mechanics. New York: Springer, 1989.
   Google Scholar