@article{ASENS_2003_4_36_4_525_0,
author = {Dehman, Belhassen and Lebeau, Gilles and Zuazua, Enrique},
title = {Stabilization and control for the subcritical semilinear wave equation},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
volume = {36},
year = {2003},
pages = {525-551},
doi = {10.1016/S0012-9593(03)00021-1},
mrnumber = {2013925},
zbl = {1036.35033},
language = {en},
url = {http://dml.mathdoc.fr/item/ASENS_2003_4_36_4_525_0}
}
Dehman, Belhassen; Lebeau, Gilles; Zuazua, Enrique. Stabilization and control for the subcritical semilinear wave equation. Annales scientifiques de l'École Normale Supérieure, Tome 36 (2003) pp. 525-551. doi : 10.1016/S0012-9593(03)00021-1. http://gdmltest.u-ga.fr/item/ASENS_2003_4_36_4_525_0/
[1] , , Opérateurs pseudo-différentiels et théorème de Nash-Moser, Savoirs Actuels, InterEditions/Editions du CNRS, 1991. | MR 1172111 | Zbl 0791.47044
[2] , , , Sharp sufficient conditions for the observation, control and stabilisation of waves from the boundary, SIAM J. Control Optim. 305 (1992) 1024-1065. | MR 1178650 | Zbl 0786.93009
[3] , Fluides parfaits incompressibles, Astérisque 209 (1995). | MR 1340046 | Zbl 0829.76003
[4] , Stabilisation pour l'équation des ondes semilinéaire, Asymptotic Anal. 27 (2001) 171-181. | MR 1852005 | Zbl 1007.35005
[5] , Microlocal defect measures, Comm. Partial Differential Equations 16 (1991) 1761-1794. | MR 1135919 | Zbl 0770.35001
[6] , Oscillation and concentration effects in semilinear dispersive wave equations, J. Funct. Anal. 41 (1) (1996) 60-98. | MR 1414374 | Zbl 0868.35075
[7] , , The global Cauchy problem for the nonlinear Klein-Gordon equation, Math. Z. 189 (1985) 487-505. | MR 786279 | Zbl 0549.35108
[8] , Regularity and asymptotic behaviour of the wave equation with a critical nonlinearity, Ann. Math. 132 (1990) 485-509. | MR 1078267 | Zbl 0736.35067
[9] , Regularity for the wave equation with critical nonlinearity, Comm. Pure Appl. Math. 45 (1992) 749-774. | MR 1162370 | Zbl 0785.35065
[10] , Stabilization of trajectories for some weakly damped hyperbolic equations, J. Differential Equations 59 (1985) 145-154. | MR 804885 | Zbl 0535.35006
[11] , Das Ansfangwertproblem im grossen für eine klasse nichtlinear wellengleichungen, Math. Z. 77 (1961) 295-308. | MR 130462 | Zbl 0111.09105
[12] , Équations des ondes amorties, in: , (Eds.), Algebraic and Geometric Methods in Math. Physics, 1996, pp. 73-109. | MR 1385677 | Zbl 0863.58068
[13] , Contrôlabilité exacte, stabilisation et perturbations de systèmes distribués, Tome 1, RMA, 8, Masson, Paris, 1988. | Zbl 0653.93002
[14] , Quelques méthodes de résolution des problèmes aux limites non-linéaires, Dunod, Paris, 1969. | MR 259693 | Zbl 0189.40603
[15] , Ondelettes et opérateurs, I & II, Hermann, Paris, 1990. | MR 1085487 | Zbl 0694.41037
[16] , Energy decay for the linear and semilinear wave equations in exterior domains with some localized dissipations, Math. Z. 4 (2001) 781-797. | MR 1872573 | Zbl 1002.35079
[17] , , Exponential decay of solutions to symmetric hyperbolic equations in bounded domains, Indiana J. Math. 24 (1974) 79-86. | MR 361461 | Zbl 0281.35012
[18] , Théorème d'unicité adapté au contrôle des solutions des problèmes hyperboliques, Comm. Partial Differential Equations 16 (1991) 789-800. | MR 1113107 | Zbl 0735.35086
[19] , Unique continuation for weak solutions of the wave equation plus a potential, J. Math. Pures Appl. 71 (1992) 455-467. | MR 1191585 | Zbl 0832.35084
[20] , , On the critical semilinear wave equation outside convex obstacles, J. Amer. Math. Soc. 8 (1995) 879-916. | MR 1308407 | Zbl 0860.35081
[21] , , Regularity results for nonlinear wave equations, Ann. Math. 138 (1993) 503-518. | MR 1247991 | Zbl 0836.35096
[22] , Restriction of Fourier transform to quadratic surfaces and decay of solutions of the wave equation, Duke Math. J. 44 (1977) 705-714. | MR 512086 | Zbl 0372.35001
[23] , The Xθs spaces and unique continuation for solutions to the semilinear wave equation, Comm. Partial Differential Equations 2 (1996) 841-887. | Zbl 0853.35017
[24] , Explicit observability estimates for the wave equation with lower order terms by means of Carleman inequalities, SIAM J. Cont. Optim. 3 (2000) 812-834. | MR 1786331 | Zbl 0982.35059
[25] , Exponential decay for semilinear wave equations with localized damping, Comm. Partial Differential Equations 15 (2) (1990) 205-235. | MR 1032629 | Zbl 0716.35010
[26] , Exact controllability for the semilinear wave equation, J. Math. Pures Appl. 69 (1) (1990) 33-55. | MR 1054122 | Zbl 0638.49017
[27] , Exponential decay for the semilinear wave equation with localized damping in unbounded domains, J. Math. Pures Appl. 70 (1992) 513-529. | MR 1146833 | Zbl 0765.35010
[28] , Exact controllability for semilinear wave equations, Ann. Inst. Henri Poincaré 10 (1) (1993) 109-129. | Numdam | MR 1212631 | Zbl 0769.93017