Exact controllability for semilinear wave equations in one space dimension
Annales de l'I.H.P. Analyse non linéaire, Volume 10 (1993) no. 1, pp. 109-129.
@article{AIHPC_1993__10_1_109_0,
     author = {Zuazua, E.},
     title = {Exact controllability for semilinear wave equations in one space dimension},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {109--129},
     publisher = {Gauthier-Villars},
     volume = {10},
     number = {1},
     year = {1993},
     zbl = {0769.93017},
     mrnumber = {1212631},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_1993__10_1_109_0/}
}
TY  - JOUR
AU  - Zuazua, E.
TI  - Exact controllability for semilinear wave equations in one space dimension
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1993
DA  - 1993///
SP  - 109
EP  - 129
VL  - 10
IS  - 1
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPC_1993__10_1_109_0/
UR  - https://zbmath.org/?q=an%3A0769.93017
UR  - https://www.ams.org/mathscinet-getitem?mr=1212631
LA  - en
ID  - AIHPC_1993__10_1_109_0
ER  - 
%0 Journal Article
%A Zuazua, E.
%T Exact controllability for semilinear wave equations in one space dimension
%J Annales de l'I.H.P. Analyse non linéaire
%D 1993
%P 109-129
%V 10
%N 1
%I Gauthier-Villars
%G en
%F AIHPC_1993__10_1_109_0
Zuazua, E. Exact controllability for semilinear wave equations in one space dimension. Annales de l'I.H.P. Analyse non linéaire, Volume 10 (1993) no. 1, pp. 109-129. http://archive.numdam.org/item/AIHPC_1993__10_1_109_0/

[BLR1] C. Bardos, G. Lebeau and J. Rauch, Contrôle et stabilisation dans les problèmes hyperboliques, Appendix II in J. L. LIONS [L2], pp. 492-537.

[BLR2] C. Bardos, G. Lebeau and J. Rauch, Sharp Sufficient Conditions for the Observation, Control and Stabilization of Waves from the Boundary, S.I.A.M. J. Control Optim., Vol. 30, 1992, pp. 1024-1065. | MR | Zbl

[CAQ] N. Carmichael and M.D. Quinn, Fixed Point Methods in Nonlinear Control, in Distributed Parametes Systems, F. KAPPEL, K. KUNISCH and W. SCHAPACHER Eds., Lecture Notes in Control and Information Sciences, #75, Springer-Verlag, Berlin, 1985, pp. 24-51. | MR | Zbl

[CH] T. Cazenave and A. Haraux, Equations d'évolution avec non-linéarité logarithmique, Ann. Fac. Sci. Toulouse, Vol. 2, 1980, pp. 21-51. | Numdam | MR | Zbl

[Ch] W.C. Chewning, Controllability of the Nonlinear Wave Equation in Several Space Variables, S.I.A.M. J. Control Optim., Vol. 14, 11976, pp. 19-25. | MR | Zbl

[Ci] M.A. Cirina, Boundary Controllability of Nonlinear Hyperbolic Systems, S.I.A.M. J. Control, Vol. 7, 1969, pp. 198-212. | MR | Zbl

[F] H.O. Fattorini, Local Controllability of a Nonlinear Wave Equation, Math. Systems Theory, Vol. 9, 1975, pp. 363-366. | MR | Zbl

[H] H. Hermes, Controllability and the Singular Problem, S.I.A.M. J. Control, Vol. 2, 1965, p. 241-260. | MR | Zbl

[LaT1] I. Lasiecka and R. Triggiani, Exact Controllability of Semilinear Abstract Systems with Applications to Wave and Plates Boundary Control Problems, Proceedings of the 28th I.E.E.E. Conference on Decision and Control, 1989, pp. 2291-2294.

[LaT2] I. Lasiecka and R. Triggiani, Exact Controllability of Semilinear Abstract Systems with Applications to Wave and Plates Boundary Control Problems, Appl. Math. & Optim., Vol. 23, 1991, p. 109-154. | Zbl

[LeM] E.B. Lee and L.W. Markus, Foundations of Optimal Control Theory, John Wiley, New York, 1967. | MR | Zbl

[L1] J.L. Lions, Contrôlabilité exacte de systèmes distribués, C. R. Acad. Sci. Paris, Vol. 302, 1986, pp. 471-475. | MR | Zbl

[L2] J.L. Lions, Contrôlabilité exacte, stabilisation et perturbations de systèmes distribués. Tome 1. Contrôlabilité exacte, Masson, RMA8, 1988. | Zbl

[L3] J.L. Lions, Exact Controllability, Stabilization and Perturbations for Distributed Systems, S.I.A.M. Rev., Vol. 30, 1988, pp. 1-68. | MR | Zbl

[Lu] D.L. Lukes, Global Controllability of Nonlinear Systems, S.I.A.M. J. Control, Vol. 10, 1972, pp. 112-126. | MR | Zbl

[M] L. Markus, Controllability of Nonlinear Processes, S.I.A.M. J. Control, Vol. 3, 1965, p. 78-90. | MR | Zbl

[N] K. Naito, Controllability of Semilinear Control Systems, S.I.A.M. J. Control Optim., Vol. 25, 1987, p. 715-722. | MR | Zbl

[NSe] K. Naito and Th.I. Seidman, Invariance of the Approximately Reachable Set Under Nonlinear Perturbations, S.I.A.M. J. Cont. Optim., Vol. 29, 1991, pp. 731- 750. | MR | Zbl

[R] D.L. Russell, Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions, S.I.A.M. Rev., Vol. 20, 1978, pp. 639-739. | MR | Zbl

[Se] Th.I. Seidman, Invariance of the Reachable Set Under Nonlinear Perturbations, S.I.A.M. J. Control Optim., Vol. 23, 1987, pp. 1173-1191. | MR | Zbl

[S] J. Simon, Compact Sets in the Space LP (0, T; B), Annali di Matematica pura ed Applicata, (IV), Vol. CXLVI, 1987, pp. 65-96. | MR | Zbl

[Z1] E. Zuazua, Contrôlabilité exacte de systèmes d'évolution non linéaires, C. R. Acad. Sci. Paris, Vol. 306, 1988, pp. 129-132. | MR | Zbl

[Z2] E. Zuazua, Exact Controllability for the Semilinear Wave Equation, J. Math. pures et appl., Vol. 69, 1990, pp. 1-32. | MR | Zbl

[Z3] E. Zuazua, An Introduction to the Exact Controllability for Distributed Systems,Textos e Notas 44 , C.M.A.F., Universidades de Lisboa, 1990. | MR

[Z4] E. Zuazua, Exact Controllability of Semilinear Distributed Systems, Proceedings of the 27th I.E.E.E. Conference on Decision and Control, 1988, pp. 1265-1268.

[Z5] E. Zuazua, Exact Boundary Controllability for the Semilinear Wave Equation, in Nonlinear Partial Differential Equations and their Applications, H. BREZIS and J. J. LIONS, Séminaire du Collège de France 1987/1988, X, Research Notes in Mathematics, Pitman, 1991, pp. 357-391. | MR | Zbl

[Z6] E. Zuazua, Contrôlabilité exacte d'une équation des ondes surlinéaire à une dimension d'espace, C. R. Acad. Sci. Paris, 311, 1990, pp. 285-290. | MR | Zbl

[Z7] E. Zuazua, Exponential Decay for Semilinear Wave Equations with Localized Damping, Comm. in P.D.E., Vol. 15, (2), 1990, pp. 205-235. | MR | Zbl