@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}, pages = {525--551}, publisher = {Elsevier}, volume = {Ser. 4, 36}, number = {4}, year = {2003}, doi = {10.1016/S0012-9593(03)00021-1}, mrnumber = {2013925}, zbl = {1036.35033}, language = {en}, url = {http://www.numdam.org/articles/10.1016/S0012-9593(03)00021-1/} }
TY - JOUR AU - Dehman, Belhassen AU - Lebeau, Gilles AU - Zuazua, Enrique TI - Stabilization and control for the subcritical semilinear wave equation JO - Annales scientifiques de l'École Normale Supérieure PY - 2003 SP - 525 EP - 551 VL - 36 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S0012-9593(03)00021-1/ DO - 10.1016/S0012-9593(03)00021-1 LA - en ID - ASENS_2003_4_36_4_525_0 ER -
%0 Journal Article %A Dehman, Belhassen %A Lebeau, Gilles %A Zuazua, Enrique %T Stabilization and control for the subcritical semilinear wave equation %J Annales scientifiques de l'École Normale Supérieure %D 2003 %P 525-551 %V 36 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/S0012-9593(03)00021-1/ %R 10.1016/S0012-9593(03)00021-1 %G en %F 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, Tome 36 (2003) no. 4, pp. 525-551. doi : 10.1016/S0012-9593(03)00021-1. http://www.numdam.org/articles/10.1016/S0012-9593(03)00021-1/
[1] Opérateurs pseudo-différentiels et théorème de Nash-Moser, Savoirs Actuels, InterEditions/Editions du CNRS, 1991. | MR | Zbl
, ,[2] Sharp sufficient conditions for the observation, control and stabilisation of waves from the boundary, SIAM J. Control Optim. 305 (1992) 1024-1065. | MR | Zbl
, , ,[3] Fluides parfaits incompressibles, Astérisque 209 (1995). | Numdam | MR | Zbl
,[4] Stabilisation pour l'équation des ondes semilinéaire, Asymptotic Anal. 27 (2001) 171-181. | MR | Zbl
,[5] Microlocal defect measures, Comm. Partial Differential Equations 16 (1991) 1761-1794. | MR | Zbl
,[6] Oscillation and concentration effects in semilinear dispersive wave equations, J. Funct. Anal. 41 (1) (1996) 60-98. | MR | Zbl
,[7] The global Cauchy problem for the nonlinear Klein-Gordon equation, Math. Z. 189 (1985) 487-505. | MR | Zbl
, ,[8] Regularity and asymptotic behaviour of the wave equation with a critical nonlinearity, Ann. Math. 132 (1990) 485-509. | MR | Zbl
,[9] Regularity for the wave equation with critical nonlinearity, Comm. Pure Appl. Math. 45 (1992) 749-774. | MR | Zbl
,[10] Stabilization of trajectories for some weakly damped hyperbolic equations, J. Differential Equations 59 (1985) 145-154. | MR | Zbl
,[11] Das Ansfangwertproblem im grossen für eine klasse nichtlinear wellengleichungen, Math. Z. 77 (1961) 295-308. | MR | Zbl
,[12] Équations des ondes amorties, in: , (Eds.), Algebraic and Geometric Methods in Math. Physics, 1996, pp. 73-109. | MR | Zbl
,[13] Contrôlabilité exacte, stabilisation et perturbations de systèmes distribués, Tome 1, RMA, 8, Masson, Paris, 1988. | Zbl
,[14] Quelques méthodes de résolution des problèmes aux limites non-linéaires, Dunod, Paris, 1969. | MR | Zbl
,[15] Ondelettes et opérateurs, I & II, Hermann, Paris, 1990. | MR | Zbl
,[16] Energy decay for the linear and semilinear wave equations in exterior domains with some localized dissipations, Math. Z. 4 (2001) 781-797. | MR | Zbl
,[17] Exponential decay of solutions to symmetric hyperbolic equations in bounded domains, Indiana J. Math. 24 (1974) 79-86. | MR | Zbl
, ,[18] Théorème d'unicité adapté au contrôle des solutions des problèmes hyperboliques, Comm. Partial Differential Equations 16 (1991) 789-800. | MR | Zbl
,[19] Unique continuation for weak solutions of the wave equation plus a potential, J. Math. Pures Appl. 71 (1992) 455-467. | MR | Zbl
,[20] On the critical semilinear wave equation outside convex obstacles, J. Amer. Math. Soc. 8 (1995) 879-916. | MR | Zbl
, ,[21] Regularity results for nonlinear wave equations, Ann. Math. 138 (1993) 503-518. | MR | Zbl
, ,[22] Restriction of Fourier transform to quadratic surfaces and decay of solutions of the wave equation, Duke Math. J. 44 (1977) 705-714. | MR | Zbl
,[23] The Xθs spaces and unique continuation for solutions to the semilinear wave equation, Comm. Partial Differential Equations 2 (1996) 841-887. | Zbl
,[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 | Zbl
,[25] Exponential decay for semilinear wave equations with localized damping, Comm. Partial Differential Equations 15 (2) (1990) 205-235. | MR | Zbl
,[26] Exact controllability for the semilinear wave equation, J. Math. Pures Appl. 69 (1) (1990) 33-55. | MR | Zbl
,[27] Exponential decay for the semilinear wave equation with localized damping in unbounded domains, J. Math. Pures Appl. 70 (1992) 513-529. | MR | Zbl
,[28] Exact controllability for semilinear wave equations, Ann. Inst. Henri Poincaré 10 (1) (1993) 109-129. | Numdam | MR | Zbl
,Cité par Sources :