东南大学学报（英文版）2009，Vol.25Issue(2)：278-285,8.
确定抛物型方程组模型中的污染点源
Determination of pollution point source in parabolic system model
摘要
Abstract
This paper considers an inverse problem for a partial differential equation to identify a pollution point source in a watershed. The mathematical model of the problem is a weakly coupled system of two linear parabolic equations for the concentrations u(x, t) and v(x, t) with an unknown point source F(x, t) =λ(t)δ(x -s) related to the concentration u(x, t), where s is the point source location and λ(t) is the amplitude of the pollution point source. Assuming that source F becomes inactive after time T*, it is proved that it can be uniquely determined by the indirect measurements {v(O, t), v(a, t), v(b, t), v(l, t),0 < t≤T, T*< T}, and, thus, the local Lipschitz stability for this inverse source problem is obtained. Based on the proof of its uniqueness, an inversion scheme is presented to determine the point source. Finally, two numerical examples are given to show the feasibility of the inversion scheme.关键词
源项反演/抛物型方程组/惟一性/局部Lipschitz稳定/污染源Key words
inverse source problem/parabolic system/uniqueness/local Lipschitz stability/pollution source分类
数理科学引用本文复制引用
王泽文..确定抛物型方程组模型中的污染点源[J].东南大学学报（英文版）,2009,25(2):278-285,8.基金项目
The National Natural Science Foundation of China(No. 10861001), the Natural Science Foundation of Jiangxi Province. （No. 10861001）
