Global weak solutions for a degenerate parabolic system modelling seawater intrusion in confined aquifers

Alkhayal, Jana; Jazar, Mustapha; Monneau, Régis

doi:10.1080/00036811.2018.1544622

Cited by 3 publications

(1 citation statement)

References 10 publications

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“…The well-posedness of (1.1) in the setting of classical solutions is addressed in [10], while nonnegative global weak solutions are constructed, by different approaches, in [3,8,9,13,14]. The rich dynamics described by the thin film Muskat problem (1.1) is very well illustrated by the laboratory experiments described in [23], but also by the numerical simulations reported in [1,2,15].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

The porous medium equation as a singular limit of the thin film Muskat problem

Laurençot¹,

Matioc²

2021

Preprint

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The singular limit of the thin film Muskat problem is performed when the density (and possibly the viscosity) of the lighter fluid vanishes and the porous medium equation is identified as the limit problem. In particular, the height of the denser fluid is shown to converge towards the solution to the porous medium equation and an explicit rate for this convergence is provided in space dimension d ≤ 4. Moreover, the limit of the height of the lighter fluid is determined in a certain regime and is given by the corresponding initial condition.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

The porous medium equation as a singular limit of the thin film Muskat problem

Laurençot¹,

Matioc²

2021

Preprint

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show abstract

Convergence of a multi-point flux approximation finite volume scheme for a sharp–diffuse interfaces model for seawater intrusion

Amaziane

Ossmani

Talali

2023

Journal of Computational and Applied Mathematics

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The porous medium equation as a singular limit of the thin film Muskat problem

Laurençot

Matioc

2022

Asymptotic Analysis

View full text Add to dashboard Cite

The singular limit of the thin film Muskat problem is performed when the density (and possibly the viscosity) of the lighter fluid vanishes and the porous medium equation is identified as the limit problem. In particular, the height of the denser fluid is shown to converge towards the solution to the porous medium equation and an explicit rate for this convergence is provided in space dimension d ⩽ 4. Moreover, the limit of the height of the lighter fluid is determined in a certain regime and is given by the corresponding initial condition.

show abstract

Global weak solutions for a degenerate parabolic system modelling seawater intrusion in confined aquifers

Cited by 3 publications

References 10 publications

The porous medium equation as a singular limit of the thin film Muskat problem

The porous medium equation as a singular limit of the thin film Muskat problem

Convergence of a multi-point flux approximation finite volume scheme for a sharp–diffuse interfaces model for seawater intrusion

The porous medium equation as a singular limit of the thin film Muskat problem

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