×

zbMATH — the first resource for mathematics

Analysis and approximation for inverse problems in contaminant transport and biodegradation models. (English) Zbl 0839.76081
Summary: We consider the problem of estimating transport and biodegradation parameters in a contaminant transport model. We develop a convergence theory for parameter identification under approximation that includes the nonlinearities inherent in the biodegradation models. The functional analytic approach provides a means for studying a variety of solute transport and biodegradation problems.

MSC:
76R50 Diffusion
86A05 Hydrology, hydrography, oceanography
76Z99 Biological fluid mechanics
35R30 Inverse problems for PDEs
PDF BibTeX XML Cite
Full Text: DOI Link
References:
[1] Banks H. T., Lecture Notes in Biomathematics 6 (1975)
[2] Banks H. T., Control:Theory and Advanced Technology 4 pp 73– (1988)
[3] DOI: 10.1007/978-1-4612-3700-6
[4] Bear J., Dynamics of Fluids in Porous Media (1972) · Zbl 1191.76001
[5] Boggs J. M., Database for the Second Macrodispersion Experiment MADE-2 (1993)
[6] DOI: 10.1029/92WR01756
[7] DOI: 10.1029/WR022i013p01973
[8] DOI: 10.1029/WR022i013p01983
[9] DOI: 10.1090/S0025-5718-1982-0637287-3
[10] DOI: 10.1029/WR025i006p01149
[11] DOI: 10.1007/BF00137855
[12] Cressie N. A., Statistics for Spatial Data (1991) · Zbl 0799.62002
[13] Freeze R. A., Groundwater (1979)
[14] DOI: 10.1137/0328057 · Zbl 0734.35152
[15] Johnson C., Numerical Solution of Partial Differential Equations by the Finite Element Method (1987) · Zbl 0628.65098
[16] DOI: 10.1029/WR025i006p01149
[17] DOI: 10.1016/0362-546X(86)90041-6 · Zbl 0619.35034
[18] Lamm P. K., Proc 5th IFAC Symposium on Control of Distributed Parameter Systems (1989)
[19] MacQuarrie K. T. B., Water Resources Research 26 pp 223– (1990)
[20] DOI: 10.1029/93WR00583
[21] Martin R. H., Nonlinear Operators and Differential Equations in Banach Spaces (1976)
[22] . Murray J. D., Mathematical Biology (1989)
[23] DOI: 10.1016/0304-3800(89)90015-X
[24] Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations 17 (1983) · Zbl 0516.47023
[25] Piskiewicz, D. 1977. New York: Oxford.
[26] Showalter R. E., Hilbert Space Methods for Partial Differential Equations (1977) · Zbl 0364.35001
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.