A multiscale method for semilinear elliptic equations

Peimin Chen, Walter Allegretto, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

At present there are many papers, based on multiscale expansion and homogenization theory, to deal with nonlinear problems with microstructure. But there is no systematic method to deal with all of the possible nonlinear partial differential equations since different nonlinear problems gives rise to different multiscale expansions parameters classes. This introduces changes in the consequent process of homogenization. In this paper, a method based on the theory of upper and lower solution is provided. It deals with nonlinear problems by reducing them to a series of linear problems. In addition numerical computations are also presented in the last part of the paper to support our theoretical analysis.
Original languageEnglish
Pages (from-to)362-371
Number of pages10
JournalJournal of Mathematical Analysis and Applications
Volume345
Issue number1
DOIs
Publication statusPublished - 1 Sep 2008
Externally publishedYes

Keywords

  • Asymptotic expansion
  • Homogenization
  • Multiscale method
  • Nonlinear elliptic equations
  • Periodic microstructure
  • Upper and lower solutions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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