A spectral approach of the null controllability of coupled non ...
A spectral approach of the null controllability of coupled non ...
A spectral approach of the null controllability of coupled non ...
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Spectral properties <strong>of</strong> A Parabolic <strong>controllability</strong> properties An applicationSpectral properties <strong>of</strong> A: localization <strong>of</strong> <strong>the</strong> spectrumPropositionLet A = A 0 + A 1 be an operator on H. Assume that(a) Re(Au, u) H ≥ λ 0 ‖u‖ 2 Hfor all u ∈ D(A),(b) A 0 : D(A 0 ) ⊂ H → H is selfadjoint, positive, with a densedomain and compact resolvent,(c) A 1 : D(A 1 ) ⊂ H → H satisfies|(A 1 u, u) H | ≤ C‖A 1/20u‖ 2qH ‖u‖2−2q Hfor q ∈ [0, 1)
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