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The hilbert uniqueness method: A retrospective

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Optimal Control of Partial Differential Equations

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 149))

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References

  1. A. Bensoussan, On the general theory of exact controllability for skew-symmetric operators, preprint.

    Google Scholar 

  2. A. Bensoussan, Some remarks on the exact controllability of Maxwell's equations, preprint.

    Google Scholar 

  3. G. Chen, Energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain, J. Math. Pures Appl., 58 (1979), 249–274.

    Google Scholar 

  4. S. Dolecki and D. L. Russell, A general theory of observation and control, SIAM J. Control and Opt., 15, (1977), 185–220.

    Google Scholar 

  5. G. Duvaut and J.-L. Lions, Les Inéquations en Mécanique et en Physique, Dunod, Paris, 1972.

    Google Scholar 

  6. L. F. Ho, Observabilité frontière de l'equation des ondes, C.R. Acad. Sci. Paris Sér. I, 302 (1986), 443–446.

    Google Scholar 

  7. O. A. Ladyzhenskaya and V. A. Solonikov, The linearization principle and invariant manifolds for problems of magnetohydrodynamics, J. Soviet Nath., 8, (1977), 384–422.

    Google Scholar 

  8. J. E. Lagnese, Decay of solutions of wave equations in a bounded region with boundary dissipation, J. Diff. Eqs. 50, (1983), 163–182.

    Google Scholar 

  9. J. E. Lagnese, Exact boundary controllability of Maxwell's equations in a general region, SIAM J. Control and Opt., 27, (1989), 374–388.

    Google Scholar 

  10. J. E. Lagnese and J.-L. Lions, Modelling, Analysis and Control of Thin Plates, Recherches en Mathématiques Appliquées, Vol. 6, Masson, Paris, 1988.

    Google Scholar 

  11. I. Lasiecka, Controllability of a viscoelastic Kirchhoff plate, Internat. Ser. in Numerical Math., 91 (1989), 237–247.

    Google Scholar 

  12. I. Lasiecka and R. Triggiani, Exact controllability of the wave equation with Neumann boundary control, Appl. Math. and Opt., 19 (1989), 243–290.

    Google Scholar 

  13. I. Lasiecka and R. Triggiani, Exact controllability of the Euler-Bernoulli equation with controls in the Dirichlet and Neumann boundary conditions: a nonconservative case, SIAM J. Control and Opt., 27 (1989), 330–372.

    Google Scholar 

  14. J.-L. Lions, Exact controllability, stabilization and perturbations for distributed parameter systems, SIAM Review, 30 (1988), 1–68.

    Google Scholar 

  15. J.-L. Lions, Contrôlabilité Exacte, Perturbations et Stabilisation de Systèmes Distribués. Tome 1, Contrôlabilité Exacte; Tome 2, Perturbations, Recherches en Mathématiques Appliquées, Vols. 8 and 9, Masson, Paris, 1988.

    Google Scholar 

  16. D. L. Russell, Review of Contrôlabilité Exacte, Perturbations et Stabilisation de Systèmes Distribués, Bull. Amer. Math. Soc., 22 (1990), 353–356.

    Google Scholar 

  17. R. Triggiani, Exact boundary controllability on L 2 (Ω) × H −1 (Ω) of the wave equation with Dirichlet boundary control action of a portion of the boundary, and related problems, Appl. Math. and Opt., 18 (1988), 241–277.

    Google Scholar 

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Karl-Heinz Hoffmann Werner Krabs

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© 1991 International Federation for Information Processing

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Lagnese, J.E. (1991). The hilbert uniqueness method: A retrospective. In: Hoffmann, KH., Krabs, W. (eds) Optimal Control of Partial Differential Equations. Lecture Notes in Control and Information Sciences, vol 149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043222

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  • DOI: https://doi.org/10.1007/BFb0043222

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