Abstract

Analysis of approaches to identification of thermal conductivity equation in partial derivatives has been performed. Conditions of uniqueness of solution to this problem are considered. The relation between the method of simple iterations of search for desired functions and the steepest descent method for bound operators has been shown. A conclusion has been made on the necessity to switch to regularization methods at incompressible mapping of solution to next iteration and for unbounded operators. A computational experiment has been performed. It shows that calculation of increments of functions via differentiation of the thermal conductivity equation with the temperature increment expressed via a residual functional is not sufficient for regularization of unstable solution. A conclusion has been made on the direction of development of the iterative variation method.

中文翻译：

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传热分布参数模型的辨识问题。第1部分

摘要

对偏导数中导热系数方程的识别方法进行了分析。考虑了该问题解的唯一性条件。已经显示了搜索所需函数的简单迭代方法与绑定算子的最速下降法之间的关系。已经得出结论，在解的不可压缩映射到下一次迭代和无界运算符时，有必要切换到正则化方法。已经进行了计算实验。它表明，通过热导率方程的微分计算函数增量与通过残差泛函表示的温度增量不足以对不稳定解进行正则化。