Null Controllability for Degenerate Parabolic Operators
Null Controllability for Degenerate Parabolic Operators
Null Controllability for Degenerate Parabolic Operators
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oadmap to null controllability• show equivalence with observability inequality{adjoint v t +div(A(x)∇v) = 0 in Q Tproblem v = 0 on Γ×]0, T [=⇒∫O∫ T ∫v 2 (x, 0) dx ≤ C T• prove observability by Carleman’s estimates > 0 large∫∫Q Ts 3 θ 3 (t)v 2} {{ }e 2sφ(x,t) dxdt ≤ C+sθ(t)|Dv| 2 +···0ωv 2 (x, t) dxdt∫ T0∫ωv 2 dxdtφ(x, t) = θ(t) [ e rψ(x) − e 2r‖ψ‖∞] any Dψ(x) ≠ 0 in O \ ω