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Analytical behaviour of 2D incompressible flow in porous media

Other TitlesAnalytical behavior of two-dimensional incompressible flow in porous media
AuthorsCórdoba, Diego ; Gancedo, Francisco; Orive, Rafael
KeywordsFlow through porous media
Flow simulation
Numerical analysis
Issue Date6-Jun-2007
PublisherAmerican Institute of Physics
CitationJ. Math. Phys. 48(6): 065206 (2007)
AbstractIn this paper we study the analytic structure of a two-dimensional mass balance equation of an incompressible fluid in a porous medium given by Darcy's law. We obtain local existence and uniqueness by the particle-trajectory method and we present different global existence criterions. These analytical results with numerical simulations are used to indicate nonformation of singularities. Moreover, blow-up results are shown in a class of solutions with infinite energy.
Description19 pages, 8 figures.-- 2000 Mathematics Subject Classification (MSC): 76S05, 76B03, 65N06.-- PACS nrs.: 47.56.+r, 47.10.Fg.-- First version of the paper presented at: International Congress of Mathematicians 2006 (Madrid, 22-30 Aug 2006), http://www.icm2006.org/v_f/AbsDef/Shorts/abs_1588.pdf.
Publisher version (URL)http://dx.doi.org/10.1063/1.2404593
Appears in Collections:(ICMAT) Artículos
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