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We study the null controllability properties of degenerate parabolic equations, when degeneracy occurs at the boundary of the domain. In space dimension 1 and 2, we obtain null controllability results under some necessary and sufficient condition on the degeneracy parameter, providing new global Carleman estimates. In space dimension 1, we are also able to study the behaviour of the controllability cost with respect of the degeneracy parameter, using properties of Bessel functions. |
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