Lebeau, Gilles; Robbiano, Luc Stabilization of the wave equation by the boundary. (Stabilisation de l’équation des ondes par le bord.) (French) Zbl 0884.58093 Duke Math. J. 86, No. 3, 465-491 (1997). The authors consider the problem of stabilization, i.e., the decreasing of the energy, for equations of wave type. Here the stabilization is obtained by a boundary dissipative condition. Estimates on the rate of the decreasing of the energy are also given. Reviewer: Marco Biroli (Monza) Cited in 2 ReviewsCited in 77 Documents MSC: 58J45 Hyperbolic equations on manifolds 35L05 Wave equation 49J20 Existence theories for optimal control problems involving partial differential equations Keywords:wave equation; stabilization PDF BibTeX XML Cite \textit{G. Lebeau} and \textit{L. Robbiano}, Duke Math. J. 86, No. 3, 465--491 (1997; Zbl 0884.58093) Full Text: DOI OpenURL References: [1] M. Abramowitz and I. Stegun, Handbook of Mathematical Functions , Nat. Bureau Stand. Appl. Math. Ser., vol. 55, Superintendent of Documents, U.S. Government Printing Office, Washington, 1964. · Zbl 0171.38503 [2] C. Bardos, G. Lebeau, and J. Rauch, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary , SIAM J. Control Optim. 30 (1992), no. 5, 1024-1065. · Zbl 0786.93009 [3] A. Haraux, Stabilization of trajectories for some weakly damped hyperbolic equations , J. Differential Equations 59 (1985), no. 2, 145-154. · Zbl 0535.35006 [4] 1 L. Hörmander, The Analysis of Linear Partial Differential Operators. III , Grundlehren Math. Wiss., vol. 274, Springer-Verlag, Berlin, 1985. · Zbl 0601.35001 [5] 2 L. Hörmander, The Analysis of Linear Partial Differential Operators. IV , Grundlehren Math. Wiss., vol. 275, Springer-Verlag, Berlin, 1985. · Zbl 0612.35001 [6] G. Lebeau, Équation des ondes amorties , Algebraic and Geometric Methods in Mathematical Physics (Kaciveli, 1993), Math. Phys. Stud., vol. 19, Kluwer Acad. Publ., Dordrecht, 1996, pp. 73-109. · Zbl 0863.58068 [7] G. Lebeau and L. Robbiano, Contrôle exact de l’équation de la chaleur , Comm. Partial Differential Equations 20 (1995), no. 1-2, 335-356. · Zbl 0819.35071 [8] L. Robbiano, Fonction de coût et contrôle des solutions des équations hyperboliques , Asymptotic Anal. 10 (1995), no. 2, 95-115. · Zbl 0882.35015 [9] D. Tataru, A priori estimates of Carleman’s type in domains with boundary , J. Math. Pures Appl. (9) 73 (1994), no. 4, 355-387. · Zbl 0835.35031 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.