Groundwater flow in a fissurised porous stratum

Michiel Bertsch; Carlo Nitsch

doi:10.3934/nhm.2010.5.765

Article Contents

2010, Volume 5, Issue 4: 765-782. Doi: 10.3934/nhm.2010.5.765

This issue Previous Article Non-existence of positive stationary solutions for a class of semi-linear PDEs with random coefficients Next Article Asymptotic analysis of the Stokes flow with variable viscosity in a thin elastic channel

Groundwater flow in a fissurised porous stratum

Michiel Bertsch^1, and
Carlo Nitsch^2,

1.
Istituto per le Applicazioni del Calcolo "M. Picone”, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185 Roma
2.
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Via Cintia, Monte S. Angelo, I-80126 Napoli

Received: February 2010

Published: December 2010

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Abstract

In [2] Barenblatt e.a. introduced a fluid model for groundwater flow in fissurised porous media. The system consists of two diffusion equations for the groundwater levels in, respectively, the porous bulk and the system of cracks. The equations are coupled by a fluid exchange term. Numerical evidence in [2, 8] suggests that the penetration depth of the fluid increases dramatically due to the presence of cracks and that the smallness of certain parameter values play a key role in this phenomenon. In the present paper we give precise estimates for the penetration depth in terms of the smallness of some of the parameters.

Keywords:

Groundwater flow,
fissurized porous medium,
system of partial differential equations,
free boundary.

Mathematics Subject Classification: Primary: 35K55; Secondary: 35B30, 35Q35, 35R35, 76S05.

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References

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