References
Lions J.-L., Controlabilite Exacte, Perturbations et Stabilization de Systemes Distribues. Vol. 1: Controlabilite Exacte, Masson, Paris (1988).
Lions J.-L., “Exact controllability, stabilisation and perturbations for distributed systems,” SIAM Rev.,30, No. 1, 1–68 (1988).
Lions J.-L., “Controlabilite exacte de systemes distribues,” Acad. Sci. Ser. I Math., No. 302, 471–475 (1986).
Èmanuilov O. Yu., “Exact controllability of hyperbolic equations. I,” Avtomatika, No. 3, 10–13 (1990).
Bardos C., Lebeau G., andRauch J., “Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary,” SIAM J. Control Optim.,30, No. 5, 1024–1065 (1992).
Komornik V., “Exact controllability and stabilization,” Lecture Notes in Control and Inform.,148, 149–192 (1990).
Lagnese J., “The Hilbert uniqueness method: A retrospective,” Lecture Notes in Control and Inform.,148, 158–181 (1990).
Hörmander L., Linear Partial Differential Operators [Russian translation], Mir, Moscow (1965).
Lasiecka I., Triggiani R., andYao P. F., “Exact controllability for second-order hyperbolic equations with variable coefficient-principal part and first-order terms,” Nonlinear Anal. Theory, Methods and Applications,30, No. 1, 111–122 (1997).
Tataru D., “Boundary controllability for conservative PDEs,” Appl. Math. Optim.,31, No. 3, 257–295 (1995).
Littman W. andTaylor S., “Smoothing evolution equations and boundary control theory,” J. Anal. Math.,59, 117–131 (1992).
Lions J.-L. andMagenes E., Inhomogeneous Boundary Value Problems and Their Applications [Russian translation], Mir, Moscow (1972).
Lions J.-L., Control of Singular Distributed Systems [Russian translation], Nauka, Moscow (1987).
Taylor M. E., Pseudodifferential Operators [Russian translation], Mir, Moscow (1985).
Additional information
The research was partially supported by the International Science Foundation (Grant M76000).
Ames (USA). Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 41, No. 4, pp. 944–959, July–August, 2000.
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Èmanuilov, O.Y. Boundary controllability of hyperbolic equations. Sib Math J 41, 785–799 (2000). https://doi.org/10.1007/BF02679705
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DOI: https://doi.org/10.1007/BF02679705