×

An inverse problem of identifying source coefficient in solute transportation. (English) Zbl 1132.35497

Summary: This paper deals with an inverse problem of identifying a source coefficient in the process of solute transport in 1D groundwater flow. With the help of an adjoint problem, the solute concentration can be made to be monotone in time by some constraints on the known data and unknown parameters. The integral identity connecting varies of the known data with corresponding changes of the unknown ones is constructed. Furthermore, by analyzing the adjoint problem with the variable separation method, a suitable norm for the unknown parameters is defined based on the integral identity by which conditional stability for the inverse problem considered here is obtained.

MSC:

35R30 Inverse problems for PDEs
35B35 Stability in context of PDEs
76S05 Flows in porous media; filtration; seepage
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1006/enfo.2001.0055 · doi:10.1006/enfo.2001.0055
[2] DOI: 10.1088/0266-5611/14/3/010 · Zbl 0917.35156 · doi:10.1088/0266-5611/14/3/010
[3] Choulli M., J. Inv. Ill-Posed Problems 12 pp 3– (2004)
[4] DOI: 10.1088/0266-5611/13/1/003 · Zbl 0867.35112 · doi:10.1088/0266-5611/13/1/003
[5] DOI: 10.1137/S0036141093259257 · Zbl 0849.35146 · doi:10.1137/S0036141093259257
[6] Isakov V., Communications on Pure and Applied Mathematics 54 pp 2– (1991)
[7] DOI: 10.1088/0266-5611/15/1/004 · Zbl 0918.35145 · doi:10.1088/0266-5611/15/1/004
[8] DOI: 10.1088/0266-5611/8/4/009 · Zbl 0755.35151 · doi:10.1088/0266-5611/8/4/009
[9] DOI: 10.1080/00036810500277926 · Zbl 1134.37321 · doi:10.1080/00036810500277926
[10] DOI: 10.1016/j.amc.2005.04.053 · Zbl 1105.35144 · doi:10.1016/j.amc.2005.04.053
[11] DOI: 10.1515/156939406779768283 · doi:10.1515/156939406779768283
[12] DOI: 10.1061/(ASCE)0733-9496(2001)127:1(1) · doi:10.1061/(ASCE)0733-9496(2001)127:1(1)
[13] DOI: 10.1016/0895-7177(95)00098-M · Zbl 0835.35157 · doi:10.1016/0895-7177(95)00098-M
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.