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**Numerical inversion of a time-dependent reaction coefficient in a soil-column infiltrating experiment.**
*(English)*
Zbl 1231.65160

Summary: This paper deals with an inverse problem of determining a time-depen -dent reaction coefficient arising from a disturbed soil-column infiltrating experiment based on measured breakthrough data. A purpose of doing such experiment is to simulate and study transport behaviors of contaminants when they vertically penetrating through the soils. Data compatibility of the inverse problem is discussed showing a sufficient condition to the solution’s monotonicity and positivity with the help of an adjoint problem. Furthermore, an optimal perturbation regularization algorithm is applied to solve the inverse problem, and two typical numerical examples are presented to support the inversion algorithm. Finally, transport model of a positive solute ion in the soil-column is investigated based on the researches to the inverse problem. An optimal reaction coefficient is determined by the inversion algorithm, and the inversion is of numerical uniqueness. The inversion results not only coincide with data compatibility of the inverse problem, but also agree with the real breakthrough data.

### MSC:

65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |

80A32 | Chemically reacting flows |

80A23 | Inverse problems in thermodynamics and heat transfer |

35R30 | Inverse problems for PDEs |

76S05 | Flows in porous media; filtration; seepage |