一类流域点污染源识别的稳定性与数值模拟

Stability and numerical simulation of pollution point source identification in a watershed

本文考虑了流域中单个点污染源识别问题的唯一性、稳定性和反演算法。该问题的数学模型为一维线性对流反应扩散方程,方程的源项F(x,t)表示了污染源是一个随时间变化的点污染源。在对污染源及测量点的先验假设下,获得了点源识别的唯一性和局部稳定性,给出了识别污染源位置s和污染强度λ(t)的计算方法。数值例子表明源项反演的算法是有效的。

In this paper, the uniqueness, stability and recovering methods of the pollution point source identification in a watershed were considered. Mathematical model of the problem is a one-dimension linear advection-dispersion-reaction equation, in which source term is expressed as F（x,t）= λ（t）σ（x-s）. The source term denotes a point pollution source which changes with time. Under the prior supposes of source term and the measured points, the uniqueness, the local stability and numerical methods for identifying the source location S and the intensity ,λ（t） were given. The numerical example shows the sufficiency of the recovering methods.