Null controllability properties of some degenerate parabolic equations.

Presentation of the problem
Ω bounded, smooth domain of R 2 (R n ) ; ω nonempty open subset
of Ω.
but non uniformly positive :
A : Ω → S 2 (R), A(x) ≥ 0,
∀x ∈ ∂Ω, det(A(x)) = 0.
Null controllability and inverse problems properties of
⎧
⎪⎨ u t − div (A(x)∇u) = h(x, t)χ ω ,
boundary conditions,
⎪⎩
initial condition
(First step to exact controllability to trajectories...)
Uniformly positive case : heat equation Lebeau-Robbiano (95),
general case : Fursikov-Imanuvilov (95,96)
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