Carleman estimates and controllability results for fully-discrete approximations of 1-D parabolic equations

12/03/2020

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by   Víctor Hernández-Santamaría, et al.

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In this paper, we prove a Carleman estimate for fully-discrete approximations of parabolic operators in which the discrete parameters h and t are connected to the large Carleman parameter. We use this estimate to obtain relaxed observability inequalities which yield, by duality, controllability results for fully-discrete linear and semilinear parabolic equations.