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Strong solutions for Richards’ equation with Cauchy conditions and constant pressure gradient

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Abstract

In this note, Richards’ equation for two layered soils is considered in a two-dimensional spatial domain. It is endowed by pressure gradient and pressure condition at the top of domain, and no condition is posed at the bottom of domain. An existence and uniqueness result of strong solutions is obtained for such a problem assuming constant pressure gradient.

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Acknowledgements

The authors want to thank Dr. Hagop Tossounian from Center for Mathematical Modeling of University of Chile, for precious conversations during the preparation and the revision of this work. Useful comments by anonymous reviewers are also acknowledged. The first author acknowledges the partial support of SmartWater Project (Grant Number 5ABY6P0), funded by Regione Puglia through the Innonetwork call.

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  1. Istituto di Ricerca sulle Acque, Consiglio Nazionale delle Ricerche, via De Blasio 5, 70132, Bari, Italy

    Marco Berardi

  2. Code Architects Automation, Via Campania 1, 70029, Santeramo in Colle, Italy

    Fabio V. Difonzo

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Correspondence to Marco Berardi.

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Berardi, M., Difonzo, F.V. Strong solutions for Richards’ equation with Cauchy conditions and constant pressure gradient. Environ Fluid Mech 20, 165–174 (2020). https://doi.org/10.1007/s10652-019-09705-w

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