1 |
J. A. D. Appleby, M. Fabrizio, B. Lazzari, and D. W. Reynolds, On exponential asymptotic stability in linear viscoelasticity, Math. Models Methods Appl. Sci. 16 (2006), no. 10, 1677-1694.
DOI
|
2 |
C. Abdallah, P. Dorato, and R. Byrne, Delayed positive feedback can stabilize oscillatory system, Proceedings of the American Control Conference, San Francisco, pp. 3106-3107, 1993.
|
3 |
F. Alabau-Boussouira, P. Cannarsa, and D. Sforza, Decay estimates for second order evolution equations with memory, J. Funct. Anal. 254 (2008), no. 5, 1342-1372.
DOI
|
4 |
M.M. Cavalcanti, A. Khemmoudj, and M. Medjden, Uniform stabilization of the damped Cauchy-Ventcel problem with variable coefficients and dynamic boundary conditions, J. Math. Anal. Appl., 328 (2007), no. 2, 900-930.
DOI
|
5 |
M. M. Cavalcanti and H. Oquendo, Frictional versus viscoelastic damping in a semilinear wave equation, SIMA J. Control Optim, 42 (2003), no. 4, 1310-1324.
DOI
|
6 |
C. M. Dafermos, An abstract Volterra equation with application to linear viscoelasticity, J. Differential Equations 7 (1970), 554-589.
DOI
|
7 |
R. Datko, J. Lagnese, and M. P. Polis, An example on the of time delays in boundary feedback stabilization of wave equations, SIAM J. Control Optim. 24 (1986), 152-156.
DOI
|
8 |
R. Gulliver, I. Lasiecka, W. Littman, and R. Triggiani, The case for differential geometry in the control of single and coupled PDEs: the structural acoustic chamber, In: Geometric Methods in Inverse Problems and PDE Control. IMA Vol. Math. Appl., vol. 137, pp. 73-181. Springer, New York, 2004.
|
9 |
B. Z. Guo and Z.C. Shao, On exponential stability of a semilinear wave equation with variable coefficients under the nonlinear boundary feedback, Nonlinear Anal. 71 (2009), no. 12, 5961-5978.
DOI
|
10 |
M. Kirane and B. Said-Houari, Existence and asymptotic stability of a viscoelastic wave equation with a delay, Z. Angew. Math. Phys. 62 (2011), no. 6, 1065-1082.
DOI
|
11 |
V. Komornik and E. Zuazua, A direct method for the boundary stabilization of the wave equation, J. Math. Pures Appl. 60 (1990), no. 1, 33-54.
|
12 |
W. J. Liu, Asymptotic behavior of solutions of time-delayed Burgers' equation, Discrete Contin. Dyn. Syst. Ser. B 2 (2002), no. 1, 47-56.
DOI
|
13 |
J. E. Munoz Rivera and J. Barbosa Sobrinho, Existence and uniform rates of decay for contact problems in viscoelasticity, Appl. Anal. 67 (1997), no. 3-4, 175-199.
DOI
|
14 |
S. Nicaise and 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), no. 5, 1561-1585.
DOI
|
15 |
S. Nicaise and C. Pignotti, Internal and boundary observability estimates for the heterogeneous Maxwells system, Appl. Math. Optim. 54 (2006), no. 1, 47-70.
DOI
|
16 |
S. Nicaise and C. Pignotti, Stabilization of the wave equation with boundary or internal distributed delay, Differential Integral Equations 21 (2008), no. 9-10, 935-958.
|
17 |
Z. H. Ning, C. X. Shen, and X. P. Zhao, Stabilization of the wave equation with variable coefficients and a delay in dissipative internal feedback, J. Math. Anal. Appl. 405 (2013), no. 1, 148-155.
DOI
|
18 |
Z. H. Ning, C. X. Shen, X. P. Zhao, H. Li, C. S. Lin, and Y. M. Zhang, Nonlinear boundary stabilization of the wave equations with variable coefficients and time dependent delay, Appl. Math. Comput. 232 (2014), 511-520.
|
19 |
J. E. M. Rivera, Asymptotic behaviour in linear viscoelasticity, Quart. Appl. Math. 52 (1994), 629-648.
|
20 |
J. E. M. Rivera and A. P. Salvatierra, Asymptotic behaviour of the energy in partially viscoelastic materials, Quart. Appl. Math. 59 (2001), 557-578.
DOI
|
21 |
I. H. Suh and Z. Bien, Use of time delay action in the controller design, IEEE Trans. Autom. Control 25 (1980), 600-503.
DOI
|
22 |
C. Q. Xu, S.P. Yung, and L. K. Li, Stabilization of wave systems with input delay in the boundary control, ESAIM Control Optim. Calc. Var. 12 (2006), no. 4, 770-785.
DOI
|
23 |
P. F. Yao, On the observability inequalities for exact controllability of wave equations with variable coefficients, SIAM J. Contr. Optim. 37 (1999), no. 5, 1568-1599.
DOI
|
24 |
P. F. Yao, Global smooth solutions for the quasilinear wave equation with boundary dissipation, J. Differential Equations 241 (2007), no. 1, 62-93.
DOI
|
25 |
P. F. Yao, Boundary controllability for the quasilinear wave equation, Appl. Math. Optim. 61 (2010), no. 2, 191-233.
DOI
|
26 |
P. F. Yao, Modeling and Control in Vibrational and Structural Dynamics, A Differential Geometric Approach, Chapman and Hall/CRC Applied Mathematics and Nonlinear Science Series. CRC Press, Boca Raton, FL, 2011.
|