Null controllability properties of some degenerate parabolic equations.
Null controllability properties of some degenerate parabolic equations.
Null controllability properties of some degenerate parabolic equations.
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Associated observability estimate<br />
The null <strong>controllability</strong> result derives from the following<br />
observability estimate :<br />
Theorem<br />
Under (H s (A)), there is <strong>some</strong> C(Ω, ω, T ) independent <strong>of</strong> α ∈ [1, 2)<br />
such that, given v T ∈ L 2 (Ω), the solution v <strong>of</strong> the adjoint problem<br />
satisfies :<br />
∫<br />
Ω<br />
⎧<br />
⎪⎨ v t + div (A(x)∇v) = 0, x ∈ Ω, t > 0<br />
A∇v(t, x) · ν = 0 on Γ,<br />
⎪⎩<br />
v(T , x) = v T (x)<br />
∫<br />
v(0, x) 2 T ∫<br />
dx ≤ e eC(Ω,ω,T )/(2−α)2 v(t, x) 2 dx dt.<br />
0<br />
ω<br />
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