We consider the problem of reconstructing distributed inputs (disturbances) in linear parabolic equations. An algorithm for solving this problem is given. An upper bound for the convergence rate is established for the case in which the input is a function of bounded variation. The algorithm combines the optimal preset and positional control methods and permits reconstruction based on inaccurate measurements of solutions of the equations at discrete time instants.

中文翻译：

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线性抛物型方程动态正则化方法的改进

我们考虑在线性抛物线方程中重构分布式输入（干扰）的问题。给出了解决这个问题的算法。在输入是有界变化的函数的情况下，建立了收敛速度的上限。该算法结合了最佳预设和位置控制方法，并允许基于离散时刻方程解的不准确测量值进行重建。