On the infiltration of rain water through the soil with runoff of the excess water.

*(English)*Zbl 1083.35107Summary: This paper deals with the modelling of the rain water infiltration through the soil above the aquifer in case of runoff of the excess water. The main feature of the model lies on the correct definition of the boundary condition on the ground surface. The latter allows to estimate, after saturation, the real amount of the water that penetrates the soil and the one which runs off. The quantity playing a key role is the so-called rain pressure, defined as the pressure exerted by the rain on the soil. Although its importance is basically theoretical and it can be neglected for practical purposes, it helps understanding the real evolution of the physical problem, providing a theoretical justification of the empirical procedures.

##### MSC:

35Q35 | PDEs in connection with fluid mechanics |

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

35R35 | Free boundary problems for PDEs |

35K60 | Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations |

86A05 | Hydrology, hydrography, oceanography |

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\textit{I. Borsi} et al., Nonlinear Anal., Real World Appl. 5, No. 5, 763--800 (2004; Zbl 1083.35107)

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