对流弥散方程的时间依赖反应系数反演及应用  

Inverse problem of determining time-dependent reaction coefficient in advection dispersion equation and its application

作　　者：李功胜[1] 贾现正[1] 张大利[1] 

机构地区：[1]山东理工大学理学院,山东淄博255049

出　　处：《应用数学与计算数学学报》2012年第3期312-331,共20页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11071148);山东省自然科学基金资助项目(ZR2011AQ014)

摘　　要：探讨了一维对流弥散方程的时间依赖反应系数函数的反演问题及其在一个土柱渗流试验中的应用.借助一个积分恒等式,讨论了正问题单调解的存在条件及反问题的数据相容性.进一步考虑一个扰动土柱试验模型模拟问题,应用一种最佳摄动量正则化算法,对反应系数函数进行了数值反演模拟,并应用于实际试验数据的反分析,反演重建结果不仅与相容性分析一致,而且与实际观测数据基本吻合.An inverse problem of determining a time-dependent reaction coef- ficient in 1-D advection dispersion equation based on the breakthrough data is dealed with in this paper. With the help of an integral identity, data compatibil- ity of the inverse problem is analyzed, and a sufficient condition to the solution＇s monotonicity of the forward problem is obtained. Furthermore, a soil-column in- filtrating experiment is investigated, and an optimal perturbation regularization algorithm is applied to solve the inverse problem. Two typical numerical examples are presented to support the inversion algorithm, and optimal reaction coefficients to the real problem are determined. The inversion results not only coincide with the data compatibility analysis, but also agree with the measured breakthrough data.

关 键 词：对流弥散方程 时间依赖反应系数 反问题 数据相容性 最佳摄动量正则化算法 数值模拟 土柱试验 数据重建 

分 类 号：O175[理学—数学] O242[理学—基础数学]