Null controllability properties of some degenerate parabolic equations.

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Joint work with - Piermarco Cannarsa, Univ. Tor Vergata, Roma 2, - Judith Vancostenoble, Univ. Toulouse 3, 2/26
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) 3/26
Page 1: Carleman estimates and applications
Page 5 and 6: An example in N-D ◮ biology : the
Page 7 and 8: ◮ α ≥ 2 : well-posed with the
Page 9 and 10: The control problem We consider ⎧
Page 11 and 12: Associated observability estimate T
Page 13 and 14: Associated observability estimate T
Page 15 and 16: Extensions ◮ more general degener
Page 17 and 18: Useful 1-D Hardy type inequalities
Page 19 and 20: A useful improved version (J. Vanco
Page 21 and 22: Useful 2-D (N-D) Hardy type inequal
Page 23 and 24: How to obtain the Carleman estimate
Page 25 and 26: But the Hardy type inequalities all

Null controllability properties of some degenerate parabolic equations.

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