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Exact controllability in short time. (English) Zbl 0676.49027
Control of boundaries and stabilization, Proc. IFIP Conf., Clermont Ferrand/Fr. 1988, Lect. Notes Control Inf. Sci. 125, 140-153 (1989).
Summary: [For the entire collection see Zbl 0672.00016.]
The Hilbert Uniqueness Method (HUM), introduced by J.-L. Lions [C. R. Acad. Sci., Paris, Sér. I 302, 471-475 (1986; Zbl 0589.49022)], allows one to obtain explicit estimates for the minimal time of exact controllability. We present here a constructive method to improve these estimates. It is based on a slightly more precise form of the usual a priori estimates in the HUM method and on an estimation method introduced recently (for different purposes) by A. Haraux [Quelques propriétés des séries lacunaires utiles dans l’étude des vibrations élastiques. H. Brézis and J. L. Lions (eds.), Res. Notes Math., Nonlinear Partial Differ. Equations Appl., Collège France Semin. 1987-1988 (to appear)].

MSC:
93B03 Attainable sets, reachability
35L05 Wave equation
93B05 Controllability
49J20 Existence theories for optimal control problems involving partial differential equations