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Carleman Estimates for a Class of Degenerate Parabolic Operators
2008
SIAM Journal of Control and Optimization
Given α ∈ [0, 2) and f ∈ L 2 ((0, T ) × (0, 1)), we derive new Carleman estimates for the degenerate parabolic problem wt The proof is based on the choice of suitable weighted functions and Hardy-type inequalities. As a consequence, for all 0 ≤ α < 2 and ω ⊂⊂ (0, 1), we deduce null controllability results for the degenerate one-dimensional heat equation ut − (x α ux)x = hχω with the same boundary conditions as above.
doi:10.1137/04062062x
fatcat:k7v56chmufg3xi625mkskf4fba