算子的分解理论及其应用

Decomposition theory of operator and its application

在Almansi理论的基础上,对求解数学弹性力学的通解过程中出现的算子分解问题进行了进一步的研究。通过引入几个函数参量推导得出了3条引理,并对Almansi理论进行了推广,得到了适用范围更广的分解方式,并给出了证明。应用该理论对一个典型的算子形式进行了分解应用。相对于已有的算子分解理论,该理论的引入使包含时间项的复杂偏微分方程可以分解为多个简单的算子方程,较其他分解理论适用范围更广,实用性更强。

Based on the Almansi theory,the problems of operator decomposition which appears in the process of solving the general solution of mathematical elastic mechanics is studied in this paper. By introducing a few function parameters,three lemmas has been derived,and applied into the Almansi theory. Therefore a more extensively applicable decomposition way is got and proofed. The theory was applied to a typical form of operator on the application of decomposition. Compared with the existing theory,the complex partial differential equation which contains time item can be decomposed into several simple operator equations by the introduction of this theory. The new decomposition theory has more extensively applicable and practical.