Null Controllability for Degenerate Parabolic Operators
Null Controllability for Degenerate Parabolic Operators
Null Controllability for Degenerate Parabolic Operators
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Carleman’s estimate 0 < α < 2w t + ( x α w x)x= f in ]0, 1[×]0, T [ + b. c.let φ(t, x) = θ(t)ψ(x) where(θ(t) =1t(T − t)) 4ψ(x) = x 2−α − 2(2 − α) 2Theorem∃ s 0 , C > 0 such that ∀s ≥ s 0∫∫Q T(sθx α w 2 x + s 3 θ 3 x 2−α w 2) e 2sφ dxdt∫∫∫ T≤ C |f | 2 e 2sφ {dxdt + C sθw2x e 2sφ} dt| x=1Q T 0