中文摘要：

探讨了孔隙与单裂隙双重介质中的一类核素迁移数学模型及其反演问题。该核素迁移模型是一个耦合的抛物型方程组定解问题。若已知排污点的核素浓度变化规律，利用Laplace变换及其逆变换方法，求得了核素迁移模型正问题的解析解；反之，由下游裂隙中某个点的实测核素浓度，利用偏微分方程的叠加原理和反问题的拟解法，反求出核素迁移模型反问题的解，即排污点的核素状态。最后，给出核素迁移模型的正问题和反问题的数值模拟。数值结果表明，正问题的解析解能够刻画核素的迁移规律，也显示出所提反问题方法能有效地反演核素污染源。

英文摘要：

A mathematical model of nuclide migration and its inverse analysis for the dual media consisting of the porosity and the single fracture media, are explored. The nuclide migration model is a coupled parabolic equations with initial and boundary conditions. If the variation of the nuclide concentration has been known at the release point, an analytical solution of the nuclide migration model is obtained by the Laplace transform and its inverse analysis. On the contrary, the solution of the inverse problem of the nuclide migration model, namely the nuclide concentration at the release point, is reconstructed by the principle of superposition of partial differential equations and the quasi-solution method of inverse problems from the measured data of nuclide concentration at one downstream point. Finally, numerical simulations for the forward and inverse problems are given. Numerical results show that the analytical solution of the forward problem can describe the variation of the nuclide migration, and the method proposed for the inverse analysis is also effective to reconstruct the nuclide pollution source.