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Carleman estimates and controllability results for fully-discrete approximations of 1-D parabolic equations (2012.02156v1)
Published 3 Dec 2020 in math.AP, cs.NA, math.NA, and math.OC
Abstract: In this paper, we prove a Carleman estimate for fully-discrete approximations of parabolic operators in which the discrete parameters $h$ and $\triangle t$ 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.