Stabilization of second order evolution equations by unbounded nonlinear feedback
Annales de l'I.H.P. Analyse non linéaire, Volume 11 (1994) no. 5, p. 485-515
@article{AIHPC_1994__11_5_485_0,
     author = {Conrad, Francis and Pierre, Michel},
     title = {Stabilization of second order evolution equations by unbounded nonlinear feedback},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {11},
     number = {5},
     year = {1994},
     pages = {485-515},
     zbl = {0841.93028},
     mrnumber = {1302277},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1994__11_5_485_0}
}
Conrad, Francis; Pierre, Michel. Stabilization of second order evolution equations by unbounded nonlinear feedback. Annales de l'I.H.P. Analyse non linéaire, Volume 11 (1994) no. 5, pp. 485-515. http://www.numdam.org/item/AIHPC_1994__11_5_485_0/

[BA-PRE] V. Barbu and Th. Precupanu, Convexity and Optimization in Banach Spaces, D. Reidel Pub. Co., Dordrecht, 1986 | MR 860772 | Zbl 0594.49001

[BE] C.D. Benchimol, A Note on Weak Stabilizability of Contraction Semi-groups, SIAM J. Contr. Opt., Vol. 16, 3, 1978, pp. 373-379. | MR 490298 | Zbl 0384.93035

[BRE] H. Brezis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland, 1973. | MR 348562 | Zbl 0252.47055

[BRE1] H. Brezis, Analyse fonctionnelle, théorie et applications, Masson, 1983. | MR 697382 | Zbl 0511.46001

[CHE] G. Chen, Energy Decay Estimates and Exact Boundary Controllability for the Wave Equation in a Bounded Domain, J. Math. Pures Appl., Vol. 58, 1979, pp. 249-274. | MR 544253 | Zbl 0414.35044

[CHE-DE] G. Chen, M. Delfour, A.M. Krall and G. Payre, Modelling, Stabilization and Control of Serially Connected Beams, SIAM J. Contr. Opt., Vol. 25, 1987, pp. 526-546. | MR 885183 | Zbl 0621.93053

[CO] F. Conrad, Stabilization of Beams by Pointwise Feedback Control, SIAM J. Contr. Opt., Vol. 28, 1990, pp. 423-437. | MR 1040468 | Zbl 0695.93089

[CO-PI] F. Conrad and M. Pierre, Stabilization of Euler-Bernoulli Beam by Nonlinear Boundary Feedback, INRIA Report RR # 1235, 1990.

[CO-PI1] F. Conrad and M. Pierre, Stabilization of Second Order Evolution Equations by Unbounded Nonlinear Feedback, INRIA Report RR # 1679, 1992. | MR 1197222

[DA] C.M. Dafermos, Application of the Invariance Principle for Compact Processes, J. Diff. Eqs., Vol. 9, 1971, pp. 291-299. | MR 289907 | Zbl 0247.34068

[DA1] C.M. Dafermos, Asymptotic Behavior of Solutions of Evolution Equations, in Nonlinear Evolution Equations, M. G. Crandall, ed., Ac. Press, 1978, pp. 103-123. | MR 513814 | Zbl 0499.35015

[DA-SLE] C.M. Dafermos and M. Slemrod, Asymptotic Behaviour of Nonlinear Contraction Semi-groups, J. Funct. Anal., Vol. 13, 1973, pp. 97-106. | MR 346611 | Zbl 0267.34062

[EL JAI-PRI] A. El Jai and T. Pritchard, Sensors and Actuators on Distributed Systems, Int. J. Control, Vol. 46, 1987, pp. 1139-1153. | MR 912980 | Zbl 0628.93033

[HA] A. Haraux, Stabilization of Trajectories for Some Weakly Damped Hyperbolic Equations, J. Diff. Eqs., Vol. 59, 2, 1985, pp. 145-154. | MR 804885 | Zbl 0535.35006

[HA1] A. Haraux, Comportement à l'infini pour certains systèmes dissipatifs non linéaires, Proc. of Royal Soc. Edinburgh, 84A, 1979, pp. 213-234. | MR 559667 | Zbl 0429.35013

[HO] L.F. Ho, Controllability and Stabilizability of Coupled Strings with Control Applied at the Coupled Points, SIAM J. Control and Optimization, Vol. 31, 6, 1993, pp. 1416-1437. | MR 1242209 | Zbl 0793.93008

[KO-ZU] V. Komornik and E. Zukzua, A Direct Method for the Boundary Stabilization of the Wave Equation J. Math. Pures et Appl., Vol. 69, 1990, pp. 33-54. | MR 1054123 | Zbl 0636.93064

[LA] I. Lasiecka, Stabilization of Wave and Plate-like Equations with Nonlinear Dissipation on the Boundary, J. Diff. Eqs., Vol. 79, 2, 1989, pp. 340-381. | MR 1000694 | Zbl 0694.35102

[LA1] I. Lasiecka, Asymptotic Behaviour of the Solution to Wave Equation with Nonlinear Damping on the Boundary, 8th Int. Conf. Analysis and Optimization of Systems, Antibes, Lect. Notes in Contr. and Inf. Sci., Vol. 111; A. Bensoussan, J. L. Lions Eds., 1988, pp. 472-483. | MR 956291 | Zbl 0675.93052

[LAG] J.E. Lagnese, Decay of Solutions of the Wave Equation in a Bounded Region with Boundary Dissipation, J. Diff. Eqs, Vol. 50, 1983, pp. 163-182. | MR 719445 | Zbl 0536.35043

[LAG1] J.E. Lagnese, Boundary Stabilization of Thin Plates, Siam (Studies in Applied Mathematics), 1989. | MR 1061153 | Zbl 0696.73034

[Q-R] J.P. Quinn and D.L. Russell, Asymptotic Stability and Energy Decay Rates for Solution of Hyperbolic Equations with Boundary Damping, Proc. Roy. Soc. Edinburgh, Sect. A, 77, 1977, pp. 97-127. | MR 473539 | Zbl 0357.35006

[RO] R.T. Rockafellar, Convex Analysis, Princeton Univ. Press, 1972. | MR 274683 | Zbl 0193.18401

[SLE] M. Slemrod, Feedback Stabilization of a Linear Control System in Hilbert Space with an a priori Bounded Control, Math. Control Signals Systems, 1988, pp. 265-285. | MR 997216 | Zbl 0676.93057

[TRI] R. Triggiani, Extension of Rank Conditions for Controllability and Observability to Banach Spaces and Unbounded Operators, SIAM J. Contr. Opt., Vol. 14, 2, 1976, pp. 313-338. | MR 479499 | Zbl 0326.93003

[Y] Y. You, Controllability and Stabilizability of Vibrating Simply Supported Plate With Pointwise Control, Adv. in Appl. Math., Vol. 10, 1989, pp. 324-343. | MR 1008559 | Zbl 0691.73039

[ZU] E. Zuazua, Uniform Stabilization of the Wave Equation by Nonlinear Boundary Feedback, SIAM J. Contr. Opt., Vol. 28, 1990, pp. 466-477. | MR 1040470 | Zbl 0695.93090