Electron. J. Differential Equations, Vol. 2022 (2022), No. 06, pp. 122.
Mathematical analysis of a DupuitRichards model
Safaa Al Nazer, Carole Rosier, Munkhgerel Tsegmid
Abstract:
This article concerns an alternative model to the 3DRichards equation to
describe the flow of water in shallow aquifers.
The model couples the two dominant types of flow existing in the aquifer.
The first is described by the classic Richards problem in the upper capillary fringe.
The second results from Dupuit's approximation after vertical integration of the conservation
laws between the bottom of the aquifer and the saturation interface.
The final model consists of a strongly coupled system of parabolictype partial differential
equations that are defined in a timedependent domain.
First, we show how taking the low compressibility of the fluid into account eliminates
the nonlinearity in the time derivative of the Richards equation.
Then, the general framework of parabolic equations is used in noncylindrical domains
to give a global in time existence result to this problem.
Submitted May 5, 2021. Published January 17, 2022.
Math Subject Classifications: 35A01, 35D30, 35K59, 35Q86, 35R35.
Key Words: DupuitRichards equations; free boundary problems; global solution;
weak solution; fluid flow modeling.
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Safaa Al Nazer
Université du Littoral Côte d'Opale, UR 2597, LMPA
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville
F62100 Calais, France
email: safaaalnazer9@gmail.com


Carole Rosier
Université du Littoral Côte d'Opale, UR 2597, LMPA
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville
F62100 Calais, France
email: Carole.Rosier@univlittoral.fr


Munkhgerel Tsegmid
School of Applied Sciences
Mongolian University of Science and Technology
Ulaanbaatar, Mongolia
email: tsemuugii@must.edu.mn

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