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Matematicheskie Zametki, 2018, Volume 103, Issue 1, Pages 49–64
DOI: https://doi.org/10.4213/mzm11452 (Mi mzm11452) 		 
Proof of Dupuit's Assumption for the Free Boundary Problem in an Inhomogeneous Porous Medium

A. Yu. Belyaev

Water Problems Institute of the Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.4213/mzm11452
Abstract: For free boundary problems describing steady groundwater flows, the asymptotic behavior of solutions is studied in the situation where the scale in one of the spatial directions is much less than that in the other directions. The convergence of solutions to a certain limit is proved. Properties of the limit solution agree with the assumption known as Dupuit's assumption in engineering applications, which customarily serves as a basis for constructing approximate models of groundwater flows in thin aquifers.
Keywords: variational inequality, Darcy's law, dam problem.
Funding agency Grant number
Russian Foundation for Basic Research 14-05-00555
Программа ОНЗ РАН III.8.10
Received: 17.11.2016
English version:
Mathematical Notes, 2018, Volume 103, Issue 1, Pages 42–53
DOI: https://doi.org/10.1134/S0001434618010054
Bibliographic databases:
Document Type: Article
UDC: 517.951+532.546
Language: Russian
Citation: A. Yu. Belyaev, “Proof of Dupuit's Assumption for the Free Boundary Problem in an Inhomogeneous Porous Medium”, Mat. Zametki, 103:1 (2018), 49–64; Math. Notes, 103:1 (2018), 42–53
Citation in format AMSBIB
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