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.

翻译：在本文中,我们证明了Carleman对抛物线操作员完全分解近似值的估计,其中离散参数($h$和$\triangle t$)与大型Carleman参数($h$和$\triangle t$)相关联。我们利用这一估计来获得宽松的可观察性不平等,通过双重性,产生全分分线线线和半线性抛物线方程的可控制性结果。