In this paper, we prove a Carleman estimate for fully discrete approximations of one-dimensional 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.

中文翻译：

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一维抛物线方程的完全离散近似的卡尔曼估计和可控性结果

在本文中，我们证明了对一维抛物线算子的完全离散近似的卡尔曼估计，其中离散参数h和 △ t与大卡尔曼参数相连。我们使用这个估计来获得宽松的可观测性不等式，通过对偶性，完全离散线性和半线性抛物线方程的可控性结果。