A spectral approach of the null controllability of coupled non ...

Spectral properties of A Parabolic controllability properties An applicationApplication to parabolic systemsPropositionSuppose |b(x)| ≥ b 0 > 0 on O and O ∩ ω ≠ ∅Then, ∃C > 0, ϕ ∈ C ∞ 0 (0, T 0) and ν ∈ (0, 1) such that∀v ∈ ( H 2 ((0, T 0 ) × Ω) ) 2 , v|(0,T0 )×∂Ω = 0, we have‖v‖ (H 1 ((ζ,T 0 −ζ)×Ω)) 2 ≤ C‖v‖1−ν (H 1 ((0,T 0 )×Ω)) 2(‖ϕB ∗ v‖ L 2 (Ω) + ‖(−∂ 2 t + A ∗ )v‖ (L 2 ((0,T 0 )×Ω)) 2 ) ν.