Null controllability properties of some degenerate parabolic equations.

Associated observability estimate
The null controllability result derives from the following
observability estimate :
Theorem
Under (H s (A)), there is some C(Ω, ω, T ) independent of α ∈ [0, 1)
such that, given v T ∈ L 2 (Ω), the solution v of the adjoint problem
satisfies :
∫
Ω
⎧
⎪⎨ v t + div (A(x)∇v) = 0, x ∈ Ω, t > 0
v(t, x) = 0 on Γ,
⎪⎩
v(T , x) = v T (x)
∫ T ∫
v(0, x) 2 dx ≤ C(Ω, ω, T ) v(t, x) 2 dx dt.
0 ω
Hence : usual observability estimate, but in the degenerate context.
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