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Controllability of Partial Differential Equations

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Figure 3.1: Wave localized at t = 0 near the endpoint x = 1 that propagates with velocity 1 to the left, bounces at x = 0 and reaches x = 1 again in a time of the order of 2.
Figure 3.2: Ray that propagates inside the domain Ω following straight lines that are reflected on the boundary according to the laws of geometrical optics.
Figure 3.3: A geometric configuration in which the Geometric Control Condi- Condi-tion is not satisfied, whatever T > 0 is
Figure 3.4: Square roots of the eigenvalues in the continuous and discrete case.

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