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On an inverse problem of pressure recovery arising from soil venting facilities. (English) Zbl 1033.35145

Summary: The technique of soil venting is commonly used for remediation of the unsaturated zone of the soil, which is contaminated by gaseous organic pollutants in the pores. We study a steady-state model with a finite number of extraction wells, where the air flow field in the subsurface is described by a linear elliptic boundary value problem with a nonlocal Neumann boundary condition, accompanied of a Dirichlet side condition, containing unknown parameters. We develop a constructive method for the parameter identification, i.e., for the determination of the unknown pressure values at the active wells from their measured total discharges.

MSC:

35R30 Inverse problems for PDEs
35J25 Boundary value problems for second-order elliptic equations
76S05 Flows in porous media; filtration; seepage
86A22 Inverse problems in geophysics
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[2] Wilson, D. J., Modeling of Insitu Techniques for Treatment of Contaminated Soils: Soil Vapor Extraction, Sparging, and Bioventing (1995), Technomic Publishing Company: Technomic Publishing Company Lancester-Basel
[3] Schumacher, S.; Slodička, M., Effective radius and underpressure of an air extraction well in a heterogeneous porous medium, Transport Porous Media, 29, 323-340 (1997)
[4] Gerke, H.; Hornung, U.; Kelanemer, Y.; Slodička, M.; Schumacher, S., Optimal Control of Soil Venting: Mathematical Modeling and Applications (1999), Birkhäuser: Birkhäuser Basel · Zbl 0919.73001
[5] Gilbarg, D.; Trudinger, N. S., Elliptic Partial Differential Equations of Second Order (1983), Springer: Springer Berlin · Zbl 0691.35001
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