A multiscale method for semilinear elliptic equations

作者：Chen Peimin; Allegretto Walter; Lin Yanping^*

来源：Journal of Mathematical Analysis and Applications, 2008, 345(1): 362-371.

DOI：10.1016/j.jmaa.2008.03.069

• nonlinear elliptic equations
• periodic microstructure
• multiscale method
• asymptotic expansion
• homogenization
• upper and lower solutions

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.

• 出版日期2008-9-1