Null Controllability for Degenerate Parabolic Operators
Null Controllability for Degenerate Parabolic Operators
Null Controllability for Degenerate Parabolic Operators
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adjoint problem <strong>for</strong> 0 < α < 2 (⋆){v t + ( x α v x)+ b. c.x= 0 in ]0, 1[×]0, T [Carleman’s estimate → localization of v(sθx∫∫Q α vx 2 + s 3 θ 3 x} 2−α{{ } v 2) ∫ T ∫e 2sφ dxdt ≤ C TT 0→0• zero order estimate too weak• need Hardy’s inequality (α ≠ 1) ∀w ∈ H 1 α(0, 1)ω|v| 2 dxdt∫ 10x α−2 w 2 dx ≤∫4 1(α − 1) 2 x α wx 2 dx0