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An inverse problem for the hydraulic properties of porous media. (English) Zbl 0870.35120

Summary: An inverse problem is formulated to determine the two coefficients in the pressure head formulation of the porous flow equation from a simple hydraulic experiment. Integral identities are derived which relate changes in the coefficients to changes in measured outputs. These identities are used to precisely define the sense in which the experimental data are able to distinguish between different porous media. It is also shown that the mapping associating input coefficient values to output data values is explicitly invertible and that there is a related output least squares problem whose solution is the solution of the inverse problem.

MSC:

35R30 Inverse problems for PDEs
35Q35 PDEs in connection with fluid mechanics
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
76S05 Flows in porous media; filtration; seepage
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