一个不适定问题的求解

复杂枝状管网的干线和支线模型都是由非线性偏微分方程组来描述,在一定条件下可以线性化,然后用解析法求解;联立模型是根据干线和支线的连接条件而建立起来的一个第一类的Volterra型积分方程组,其解一般不具有稳定性,为了获得稳定的解,本文采用吉洪诺夫正则化求解法。通过对四川某局部管网进行了实际模拟分析,证明本文方法是可行的。

SOLUTION OF ONE ILL-POSED PROBLEM

Mathematical models of the mainline and branches of complex branch-like pipeline network system are nonlinear partial differential equation systems. In some cases, the equation systems can be linearrized, and then be solved with analytical methods. The simultaneous mathematical model is a Volterra integral equation system of the first kind based on the relation connection conditions between the mainline and the branches. Usually the solution of integral equation of the first kind is not stationary, it must be solved with particular methods.Therefore,the method in this paper is proved reliable and practicable.