Institute of Mathematics

References:
[1] C. Abdallah, P. Dorato, J. Benitez-Read, R. Byrne: Delayed positive feedback can stabilize oscillatory systems. American Control Conference (ACC). IEEE, Piscataway (1993), 3106-3107. DOI 10.23919/ACC.1993.4793475
[2] E. M. Ait Benhassi, K. Ammari, S. Boulite, L. Maniar: Feedback stabilization of a class of evolution equations with delay. J. Evol. Equ. 9 (2009), 103-121. DOI 10.1007/s00028-009-0004-z | MR 2501354 | Zbl 1239.93092
[3] T. A. Apalara: Well-posedness and exponential stability for a linear damped Timoshenko system with second sound and internal distributed delay. Electron. J. Differ. Equ. 2014 (2014), Article ID 254, 15 pages. MR 3291754 | Zbl 1315.35031
[4] T. A. Apalara: Asymptotic behavior of weakly dissipative Timoshenko system with internal constant delay feedbacks. Appl. Anal. 95 (2016), 187-202. DOI 10.1080/00036811.2014.1000314 | MR 3426195 | Zbl 1336.35053
[5] T. A. Apalara: Uniform decay in weakly dissipative Timoshenko system with internal distributed delay feedbacks. Acta Math. Sci., Ser. B, Engl. Ed. 36 (2016), 815-830. DOI 10.1016/S0252-9602(16)30042-X | MR 3479257 | Zbl 1363.35238
[6] T. A. Apalara: Uniform stability of a laminated beam with structural damping and second sound. Z. Angew. Math. Phys. 68 (2017), Article ID 41, 16 pages. DOI 10.1007/s00033-017-0784-x | MR 3615474 | Zbl 1379.35182
[7] T. A. Apalara: On the stability of a thermoelastic laminated beam. Acta Math. Sci., Ser. B, Engl. Ed. 39 (2019), 1517-1524. DOI 10.1007/s10473-019-0604-9 | MR 4069832
[8] T. A. Apalara, 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. 71 (2015), 449-472. DOI 10.1007/s00245-014-9266-0 | MR 3346709 | Zbl 1326.35033
[9] H. Brezis: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York (2011). DOI 10.1007/978-0-387-70914-7 | MR 2759829 | Zbl 1220.46002
[10] X.-G. Cao, D.-Y. Liu, G.-Q. Xu: Easy test for stability of laminated beams with structural damping and boundary feedback controls. J. Dyn. Control Syst. 13 (2007), 313-336. DOI 10.1007/s10883-007-9022-8 | MR 2337280 | Zbl 1129.93010
[11] Z. Chen, W. Liu, D. Chen: General decay rates for a laminated beam with memory. Taiwanese J. Math. 23 (2019), 1227-1252. DOI 10.11650/tjm/181109 | MR 4012377 | Zbl 1425.74254
[12] R. Datko, J. Lagnese, M. P. Polis: An example on the effect of time delays in boundary feedback stabilization of wave equations. SIAM J. Control Optim. 24 (1986), 152-156. DOI 10.1137/0324007 | MR 818942 | Zbl 0592.93047
[13] B. Feng: Well-posedness and exponential decay for laminated Timoshenko beams with time delays and boundary feedbacks. Math. Methods Appl. Sci. 41 (2018), 1162-1174. DOI 10.1002/mma.4655 | MR 3762342 | Zbl 1403.35163
[14] E. Fridman, S. Nicaise, J. Valein: Stabilization of second order evolution equations with unbounded feedback with time-dependent delay. SIAM J. Control Optim. 48 (2010), 5028-5052. DOI 10.1137/090762105 | MR 2735515 | Zbl 1214.93081
[15] S. W. Hansen, R. D. Spies: Structural damping in laminated beams due to interfacial slip. J. Sound Vib. 204 (1997), 183-202. DOI 10.1006/jsvi.1996.0913
[16] M. Kirane, B. Said-Houari: Existence and asymptotic stability of a viscoelastic wave equation with a delay. Z. Angew. Math. Phys. 62 (2011), 1065-1082. DOI 10.1007/s00033-011-0145-0 | MR 2860945 | Zbl 1242.35163
[17] V. Komornik, E. Zuazua: A direct method for the boundary stabilization of the wave equation. J. Math. Pures Appl., IX. Sér. 69 (1990), 35-54. MR 1054123 | Zbl 0636.93064
[18] I. Lasiecka: Global uniform decay rates for the solutions to wave equation with nonlinear boundary conditions. Appl. Anal. 47 (1992), 191-212. DOI 10.1080/00036819208840140 | MR 1333954 | Zbl 0788.35008
[19] Z. Liu, S. Zheng: Semigroups Associated with Dissipative Systems. Chapman & Hall/CRC Research Notes in Mathematics 398. Chapman & Hall/CRC, Boca Raton (1999). MR 1681343 | Zbl 0924.73003
[20] A. Lo, N.-E. Tatar: Stabilization of laminated beams with interfacial slip. Electron. J. Differ. Equ. 2015 (2015), Article ID 129, 14 pages. MR 3358501 | Zbl 1321.35231
[21] A. Lo, N.-E. Tatar: Uniform stability of a laminated beam with structural memory. Qual. Theory Dyn. Syst. 15 (2016), 517-540. DOI 10.1007/s12346-015-0147-y | MR 3563434 | Zbl 1383.74056
[22] M. I. Mustafa: Uniform stability for thermoelastic systems with boundary time-varying delay. J. Math. Anal. Appl. 383 (2011), 490-498. DOI 10.1016/j.jmaa.2011.05.066 | MR 2812399 | Zbl 1222.35034
[23] M. I. Mustafa: Boundary control of laminated beams with interfacial slip. J. Math. Phys. 59 (2018), Article ID 051508, 9 pages. DOI 10.1063/1.5017923 | MR 3806429 | Zbl 1391.74124
[24] M. I. Mustafa: Laminated Timoshenko beams with viscoelastic damping. J. Math. Anal. Appl. 466 (2018), 619-641. DOI 10.1016/j.jmaa.2018.06.016 | MR 3818134 | Zbl 06897084
[25] S. Nicaise, C. Pignotti: Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks. SIAM J. Control Optim. 45 (2006), 1561-1585. DOI 10.1137/060648891 | MR 2272156 | Zbl 1180.35095
[26] S. Nicaise, C. Pignotti: Interior feedback stabilization of wave equations with time dependent delay. Electron. J. Differ. Equ. 2011 (2011), Article ID 41, 20 pages. MR 2788660 | Zbl 1215.35098
[27] S. Nicaise, C. Pignotti, J. Valein: Exponential stability of the wave equation with boundary time-varying delay. Discrete Contin. Dyn. Syst., Ser. S 4 (2011), 693-722. DOI 10.3934/dcdss.2011.4.693 | MR 2746429 | Zbl 1215.35030
[28] S. Nicaise, J. Valein, E. Fridman: Stability of the heat and of the wave equations with boundary time-varying delays. Discrete Contin. Dyn. Syst., Ser. S 2 (2009), 559-581. DOI 10.3934/dcdss.2009.2.559 | MR 2525768 | Zbl 1171.93029
[29] C. Pignotti: A note on stabilization of locally damped wave equations with time delay. Syst. Control Lett. 61 (2012), 92-97. DOI 10.1016/j.sysconle.2011.09.016 | MR 2878692 | Zbl 1250.93103
[30] C. A. Raposo: Exponential stability for a structure with interfacial slip and frictional damping. Appl. Math. Lett. 53 (2016), 85-91. DOI 10.1016/j.aml.2015.10.005 | MR 3426559 | Zbl 1332.35042
[31] B. Said-Houari, Y. Laskri: A stability result of a Timoshenko system with a delay term in the internal feedback. Appl. Math. Comput. 217 (2010), 2857-2869. DOI 10.1016/j.amc.2010.08.021 | MR 2733729 | Zbl 1342.74086
[32] N.-E. Tatar: Stabilization of a laminated beam with interfacial slip by boundary controls. Bound. Value Probl. 2015 (2015), Article ID 169, 11 pages. DOI 10.1186/s13661-015-0432-3 | MR 3411322 | Zbl 1338.35037
[33] J.-M. Wang, G.-Q. Xu, S.-P. Yung: Exponential stabilization of laminated beams with structural damping and boundary feedback controls. SIAM J. Control Optim. 44 (2005), 1575-1597. DOI 10.1137/040610003 | MR 2193496 | Zbl 1132.93021
[34] G. Q. Xu, S. P. Yung, L. K. Li: Stabilization of wave systems with input delay in the boundary control. ESAIM, Control Optim. Calc. Var. 12 (2006), 770-785. DOI 10.1051/cocv:2006021 | MR 2266817 | Zbl 1105.35016
[35] Q. Zhang, M. Ran, D. Xu: Analysis of the compact difference scheme for the semilinear fractional partial differential equation with time delay. Appl. Anal. 96 (2017), 1867-1884. DOI 10.1080/00036811.2016.1197914 | MR 3663769 | Zbl 1373.65061
[36] E. Zuazua: Uniform stabilization of the wave equation by nonlinear boundary feedback. SIAM J. Control Optim. 28 (1990), 466-477. DOI 10.1137/0328025 | MR 1040470 | Zbl 0695.93090