Stabilization and control for the subcritical semilinear wave equation
Annales scientifiques de l'École Normale Supérieure, Série 4, Volume 36 (2003) no. 4, p. 525-551
@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},
     publisher = {Elsevier},
     volume = {Ser. 4, 36},
     number = {4},
     year = {2003},
     pages = {525-551},
     doi = {10.1016/S0012-9593(03)00021-1},
     zbl = {1036.35033},
     mrnumber = {2013925},
     language = {en},
     url = {http://www.numdam.org/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, Série 4, Volume 36 (2003) no. 4, pp. 525-551. doi : 10.1016/S0012-9593(03)00021-1. http://www.numdam.org/item/ASENS_2003_4_36_4_525_0/

[1] Alinhac S., Gérard P., Opérateurs pseudo-différentiels et théorème de Nash-Moser, Savoirs Actuels, InterEditions/Editions du CNRS, 1991. | MR 1172111 | Zbl 0791.47044

[2] Bardos C., Lebeau G., Rauch J., 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] Chemin J.Y., Fluides parfaits incompressibles, Astérisque 209 (1995). | MR 1340046 | Zbl 0829.76003

[4] Dehman B., Stabilisation pour l'équation des ondes semilinéaire, Asymptotic Anal. 27 (2001) 171-181. | MR 1852005 | Zbl 1007.35005

[5] Gérard P., Microlocal defect measures, Comm. Partial Differential Equations 16 (1991) 1761-1794. | MR 1135919 | Zbl 0770.35001

[6] Gérard P., Oscillation and concentration effects in semilinear dispersive wave equations, J. Funct. Anal. 41 (1) (1996) 60-98. | MR 1414374 | Zbl 0868.35075

[7] Ginibre J., Velo G., The global Cauchy problem for the nonlinear Klein-Gordon equation, Math. Z. 189 (1985) 487-505. | MR 786279 | Zbl 0549.35108

[8] Grillakis M., Regularity and asymptotic behaviour of the wave equation with a critical nonlinearity, Ann. Math. 132 (1990) 485-509. | MR 1078267 | Zbl 0736.35067

[9] Grillakis M., Regularity for the wave equation with critical nonlinearity, Comm. Pure Appl. Math. 45 (1992) 749-774. | MR 1162370 | Zbl 0785.35065

[10] Haraux A., Stabilization of trajectories for some weakly damped hyperbolic equations, J. Differential Equations 59 (1985) 145-154. | MR 804885 | Zbl 0535.35006

[11] Jörgens K., Das Ansfangwertproblem im grossen für eine klasse nichtlinear wellengleichungen, Math. Z. 77 (1961) 295-308. | MR 130462 | Zbl 0111.09105

[12] Lebeau G., Équations des ondes amorties, in: Boutet De Monvel A., Marchenko V. (Eds.), Algebraic and Geometric Methods in Math. Physics, 1996, pp. 73-109. | MR 1385677 | Zbl 0863.58068

[13] Lions J.-L., Contrôlabilité exacte, stabilisation et perturbations de systèmes distribués, Tome 1, RMA, 8, Masson, Paris, 1988. | Zbl 0653.93002

[14] Lions J.-L., Quelques méthodes de résolution des problèmes aux limites non-linéaires, Dunod, Paris, 1969. | MR 259693 | Zbl 0189.40603

[15] Meyer Y., Ondelettes et opérateurs, I & II, Hermann, Paris, 1990. | MR 1085487 | Zbl 0694.41037

[16] Nakao M., 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] Rauch J., Taylor M., Exponential decay of solutions to symmetric hyperbolic equations in bounded domains, Indiana J. Math. 24 (1974) 79-86. | MR 361461 | Zbl 0281.35012

[18] Robbiano L., 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] Ruiz A., 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] Smith H., Sogge C., On the critical semilinear wave equation outside convex obstacles, J. Amer. Math. Soc. 8 (1995) 879-916. | MR 1308407 | Zbl 0860.35081

[21] Shatah J., Struwe M., Regularity results for nonlinear wave equations, Ann. Math. 138 (1993) 503-518. | MR 1247991 | Zbl 0836.35096

[22] Strichartz R., 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] Tataru D., 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] Zhang X., 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] Zuazua E., Exponential decay for semilinear wave equations with localized damping, Comm. Partial Differential Equations 15 (2) (1990) 205-235. | MR 1032629 | Zbl 0716.35010

[26] Zuazua E., Exact controllability for the semilinear wave equation, J. Math. Pures Appl. 69 (1) (1990) 33-55. | MR 1054122 | Zbl 0638.49017

[27] Zuazua E., 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] Zuazua E., Exact controllability for semilinear wave equations, Ann. Inst. Henri Poincaré 10 (1) (1993) 109-129. | Numdam | MR 1212631 | Zbl 0769.93017