Abstract
We consider the exact controllability of Maxwell’s equations in a general region. Combining the frequency domain condition developed recently by Liu [11] and the multiplier techniques, we show that the system has exact internal controllability when the control is distributed and acts in an ε-neighborhood of the boundary.
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References
A. Bensoussan, Some remarks on the exact controllability of Maxwell’s equations. Differential Equations and Control Theory (ed. V. Barbu), Pitman Res. Notes Math. Ser.250, 1991, 17–29.
G. Chen, S.A. Fulling, F.J. Narcowich and S. Sun, Exponential decay of energy of evolution equations with locally distributed damping. SIAM J. Appl. Math.,51 (1991), 266–301.
L.F. Ho, Exact controllability of the one-dimensional wave equation with locally distributed control. SIAM J. Control Optim.,28 (1990), 733–748.
B.V. Kapitonov, Stabilization and exact boundary controllability for Maxwell’s equations. SIAM J. Control Optim.,32 (1994), 408–420.
K.A. Kime, Boundary controllability of Maxwell’s equation in a spherical region. SIAM J. Control Optim.,28 (1990), 294–319.
V. Komornik, Boundary stabilization, observation and control of Maxwell’s equations. PanAmer. Math. J.,4 (1994), 47–61.
O.A. Ladyzhenskaya and V.A. Solonnikov, The linearization principle and invariant manifolds for problems of magneto-hydrodynamics. J. Soviet. Math.,8 (1977), 384–422.
J.E. Lagnese, Control of wave processes with distributed controls supported on a subregion. SIAM J. Control Optim.,21 (1983), 68–85.
J.E. Lagnese, Exact boundary controllability of Maxwell’s equations in a general region. SIAM J. Control Optim.,27 (1989), 374–388.
J.L. Lions, Exact controllability, stabilization and perturbations for distributed system. SIAM Rev.,30 (1988), 1–68.
K.S. Liu, Locally distributed control and damping for the conservative systems. Preprint.
O. Nalin, Exact controllability on the boundary of Maxwell’s equations. C. R. Acad. Sci. Paris,309 (1989), 811–815.
D.L. Russell, Controllability and stabilizability theory for linear partial differential equations: recent progress and open questions. SIAM Rev.,20 (1978), 639–739.
D.L. Russell, The Dirichlet-Neumann boundary control problem associated with Maxwell’s equation in a cylindrical region. SIAM J. Control Optim.,24 (1986), 199–219.
Q. Zhou and M. Yamamoto, Hautus condition on the exact controllability of conservative systems. To appear in Intern. J. Control.
E. Zuazua, Contrôlabilité exact interne de l’équation des ondes. Collection RMA, Masson, Paris, 1988.
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The author is supported by the Japanese Government Scholarship.
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Zhou, Q. Exact internal controllability of Maxwell’s equations. Japan J. Indust. Appl. Math. 14, 245–256 (1997). https://doi.org/10.1007/BF03167266
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DOI: https://doi.org/10.1007/BF03167266