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MATHEMATICA BOHEMICA, Vol. 126, No. 2, pp. 307-322 (2001)
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# On the solution of some inverse problems in infiltration

## D. Constales, J. Kacur

* D. Constales*, University of Ghent, Department for Mathematical Analysis, Galglaan 2, B-9000 Gent, Belgium, e-mail: ` dcons@world.std.com`, * J. Kacur*, Faculty of Mathematics and Physics, Comenius University Bratislava, Mlynska dolina, 842 15 Bratislava, Slovakia, e-mail: ` kacur@fmph.uniba.sk`

**Abstract:**
In this paper we discuss inverse problems in infiltration. We propose an efficient method for identification of model parameters, e.g., soil parameters for unsaturated porous media. Our concept is strongly based on the finite speed of propagation of the wetness front during the infiltration into a dry region. We determine the unknown parameters from the corresponding ODE system arising from the original porous media equation. We use the automatic differentiation implemented in the ODE solver LSODA. Several numerical experiments are included.

**Keywords:** porous media equation, inverse problems, Richard's equation

**Classification (MSC2000):** 35R35, 49M15, 49N45

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