Convergence in L-p space for the homogenization problems of elliptic and parabolic equations in the plane

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We study the convergence rate of an asymptotic expansion for the elliptic and parabolic operators with rapidly oscillating coefficients. First we propose homogenized expansions which are convolution forms of Green function and given force term of elliptic equation. Then, using local L-p-theory, the growth rate of the perturbation of Green function is found. From the representation of elliptic solution by Green function, we estimate the convergence rate in L-p space of the homogenized expansions to the exact solution. Finally, we consider L-2 (0, T : H-1 (Ohm)) or L-infinity (Ohm x (0, T)) convergence rate of the first order approximation for parabolic homogenization problems. (C) 2003 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2003-11
Language
English
Article Type
Article
Citation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.287, no.2, pp.321 - 336

ISSN
0022-247X
URI
http://hdl.handle.net/10203/8500
Appears in Collection
MA-Journal Papers(저널논문)
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