Convergence in LP space for the homogenization problems of elliptic and parabolic equations in the plane

Hi Jun Choe, Ki Bok Kong, Chang Ock Lee

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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 Lp-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 Lp space of the homogenized expansions to the exact solution. Finally, we consider L2 (0, T : H1 (Ω)) or L(Ω × (0, T)) convergence rate of the first order approximation for parabolic homogenization problems.

Original languageEnglish
Pages (from-to)321-336
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Volume287
Issue number2
DOIs
Publication statusPublished - 2003 Nov 15

Fingerprint

Lp Spaces
Green's function
Homogenization
Elliptic Equations
Parabolic Equation
Rate of Convergence
Oscillating Coefficients
Parabolic Operator
Convolution
Elliptic Operator
Asymptotic Expansion
Convergence Rate
Exact Solution
First-order
Perturbation
Term
Approximation
Estimate

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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abstract = "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 Lp-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 Lp space of the homogenized expansions to the exact solution. Finally, we consider L2 (0, T : H1 (Ω)) or L∞(Ω × (0, T)) convergence rate of the first order approximation for parabolic homogenization problems.",
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Convergence in LP space for the homogenization problems of elliptic and parabolic equations in the plane. / Choe, Hi Jun; Kong, Ki Bok; Lee, Chang Ock.

In: Journal of Mathematical Analysis and Applications, Vol. 287, No. 2, 15.11.2003, p. 321-336.

Research output: Contribution to journalArticle

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