Stabilization and control for the subcritical semilinear wave equation
Belhassen Dehman; Gilles Lebeau; Enrique Zuazua
Annales scientifiques de l'École Normale Supérieure (2003)
- Volume: 36, Issue: 4, page 525-551
- ISSN: 0012-9593
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topDehman, Belhassen, Lebeau, Gilles, and Zuazua, Enrique. "Stabilization and control for the subcritical semilinear wave equation." Annales scientifiques de l'École Normale Supérieure 36.4 (2003): 525-551. <http://eudml.org/doc/82609>.
@article{Dehman2003,
author = {Dehman, Belhassen, Lebeau, Gilles, Zuazua, Enrique},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {exponential decay; finite energy solutions; controllability},
language = {eng},
number = {4},
pages = {525-551},
publisher = {Elsevier},
title = {Stabilization and control for the subcritical semilinear wave equation},
url = {http://eudml.org/doc/82609},
volume = {36},
year = {2003},
}
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
PB - Elsevier
VL - 36
IS - 4
SP - 525
EP - 551
LA - eng
KW - exponential decay; finite energy solutions; controllability
UR - http://eudml.org/doc/82609
ER -
References
top- [1] Alinhac S., Gérard P., Opérateurs pseudo-différentiels et théorème de Nash–Moser, Savoirs Actuels, InterEditions/Editions du CNRS, 1991. Zbl0791.47044MR1172111
- [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. Zbl0786.93009MR1178650
- [3] Chemin J.Y., Fluides parfaits incompressibles, Astérisque209 (1995). Zbl0829.76003MR1340046
- [4] Dehman B., Stabilisation pour l'équation des ondes semilinéaire, Asymptotic Anal.27 (2001) 171-181. Zbl1007.35005MR1852005
- [5] Gérard P., Microlocal defect measures, Comm. Partial Differential Equations16 (1991) 1761-1794. Zbl0770.35001MR1135919
- [6] Gérard P., Oscillation and concentration effects in semilinear dispersive wave equations, J. Funct. Anal.41 (1) (1996) 60-98. Zbl0868.35075MR1414374
- [7] Ginibre J., Velo G., The global Cauchy problem for the nonlinear Klein–Gordon equation, Math. Z.189 (1985) 487-505. Zbl0549.35108MR786279
- [8] Grillakis M., Regularity and asymptotic behaviour of the wave equation with a critical nonlinearity, Ann. Math.132 (1990) 485-509. Zbl0736.35067MR1078267
- [9] Grillakis M., Regularity for the wave equation with critical nonlinearity, Comm. Pure Appl. Math.45 (1992) 749-774. Zbl0785.35065MR1162370
- [10] Haraux A., Stabilization of trajectories for some weakly damped hyperbolic equations, J. Differential Equations59 (1985) 145-154. Zbl0535.35006MR804885
- [11] Jörgens K., Das Ansfangwertproblem im grossen für eine klasse nichtlinear wellengleichungen, Math. Z.77 (1961) 295-308. Zbl0111.09105MR130462
- [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. Zbl0863.58068MR1385677
- [13] Lions J.-L., Contrôlabilité exacte, stabilisation et perturbations de systèmes distribués, Tome 1, RMA, 8, Masson, Paris, 1988. Zbl0653.93002
- [14] Lions J.-L., Quelques méthodes de résolution des problèmes aux limites non-linéaires, Dunod, Paris, 1969. Zbl0189.40603MR259693
- [15] Meyer Y., Ondelettes et opérateurs, I & II, Hermann, Paris, 1990. Zbl0694.41037MR1085487
- [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. Zbl1002.35079MR1872573
- [17] Rauch J., Taylor M., Exponential decay of solutions to symmetric hyperbolic equations in bounded domains, Indiana J. Math.24 (1974) 79-86. Zbl0281.35012MR361461
- [18] Robbiano L., Théorème d'unicité adapté au contrôle des solutions des problèmes hyperboliques, Comm. Partial Differential Equations16 (1991) 789-800. Zbl0735.35086MR1113107
- [19] Ruiz A., Unique continuation for weak solutions of the wave equation plus a potential, J. Math. Pures Appl.71 (1992) 455-467. Zbl0832.35084MR1191585
- [20] Smith H., Sogge C., On the critical semilinear wave equation outside convex obstacles, J. Amer. Math. Soc.8 (1995) 879-916. Zbl0860.35081MR1308407
- [21] Shatah J., Struwe M., Regularity results for nonlinear wave equations, Ann. Math.138 (1993) 503-518. Zbl0836.35096MR1247991
- [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. Zbl0372.35001MR512086
- [23] Tataru D., The Xθs spaces and unique continuation for solutions to the semilinear wave equation, Comm. Partial Differential Equations2 (1996) 841-887. Zbl0853.35017
- [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. Zbl0982.35059MR1786331
- [25] Zuazua E., Exponential decay for semilinear wave equations with localized damping, Comm. Partial Differential Equations15 (2) (1990) 205-235. Zbl0716.35010MR1032629
- [26] Zuazua E., Exact controllability for the semilinear wave equation, J. Math. Pures Appl.69 (1) (1990) 33-55. Zbl0638.49017MR1054122
- [27] Zuazua E., Exponential decay for the semilinear wave equation with localized damping in unbounded domains, J. Math. Pures Appl.70 (1992) 513-529. Zbl0765.35010MR1146833
- [28] Zuazua E., Exact controllability for semilinear wave equations, Ann. Inst. Henri Poincaré10 (1) (1993) 109-129. Zbl0769.93017MR1212631
Citations in EuDML Documents
top- Ademir Fernando Pazoto, Unique continuation and decay for the Korteweg-de Vries equation with localized damping
- Ademir Fernando Pazoto, Unique continuation and decay for the Korteweg-de Vries equation with localized damping
- Camille Laurent, Global controllability and stabilization for the nonlinear Schrödinger equation on an interval
- Louis Tebou, A Carleman estimates based approach for the stabilization of some locally damped semilinear hyperbolic equations
- Camille Laurent, On stabilization and control for the critical Klein-Gordon equation on a 3-D compact manifold
- Louis Tebou, A Carleman estimates based approach for the stabilization of some locally damped semilinear hyperbolic equations
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