中文摘要：

考虑了在流域中确定单个污染点源的偏微分方程反问题．该反问题的数学模型是关于浓度u（x，t）和v（x，t）的弱耦合线性抛物型方程组，其中关于浓度u（x，t）的点源F（x，t）=λ（t）δ（x—s）是未知的，这里S表示点源位置，λ（t）表示污染点源的排放强度．在已知污染源于时刻T＊停止排放的条件下，证明了F（x，t）=λ（t）δ（x-s）可由间接测量数据{V（0，t），v（a，t），v（b，t），v（l，t），0〈t≤T，T＊〈T}惟一决定，且该反问题是局部Lipschitz稳定的．基于惟一性的证明方法，提出了决定点源的反演算法．最后，给出的2个数值例子表明了反演算法是可行的．

英文摘要：

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） = A（ t）δ（x- s） related to the concentration u（x, t）, where s is the point source location and A（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（0, 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.