The identification of a time dependent sorption parameter from soil column experiments

Soil column studies are used frequently in seeking to understand the behavior of a particular contaminant in a saturated homogeneous soil of a given type. The concentration of the contaminant is modeled by a parabolic partial differential equation. We seek to identify the sorption partitioning coefficient as a function of time from limited boundary data. We discuss an output least squares formulation of the problem with Tikhonov regularization. We explicitly characterize a source condition that determines the rate of convergence of the method. Numerical examples are presented.