Carleman Estimates for a Class of Degenerate Parabolic Operators

P. Cannarsa, P. Martinez, J. Vancostenoble
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