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Elliptic equations in highly heterogeneous porous media
Author(s) -
Yeh LiMing
Publication year - 2009
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1163
Subject(s) - mathematics , lipschitz continuity , mathematical analysis , matrix (chemical analysis) , porous medium , norm (philosophy) , block (permutation group theory) , domain (mathematical analysis) , porosity , rate of convergence , convergence (economics) , lipschitz domain , elliptic curve , geometry , composite material , computer science , materials science , telecommunications , channel (broadcasting) , political science , law , economics , economic growth
Uniform estimate and convergence for highly heterogeneous elliptic equations are concerned. The domain considered consists of a connected fractured subregion (with high permeability) and a disconnected matrix block subregion (with low permeability). Let ε denote the size ratio of one matrix block to the whole domain and let the permeability ratio of the matrix block region to the fractured region be of the order ε 2 . In the fractured region, uniform Hölder and uniform Lipschitz estimates in ε of the elliptic solutions are derived; the convergence of the solutions in L ∞ norm is obtained as well. Copyright © 2009 John Wiley & Sons, Ltd.