Homogenization of biharmonic equations in domains perforated with tiny holes

Article type: Research Article

Authors: Huang, Chaocheng

Affiliations: Department of Mathematics and Statistics, Wright State University, Dayton, Ohio 45435, USA

Abstract: This paper deals with the homogenization of the biharmonic equation Δ2u=f in a domain containing randomly distributed tiny holes, with the Dirichlet boundary conditions. The size σ of the holes is assumed to be much smaller compared to the average distance ε between any two adjacent holes. We prove that as ε,σ→0, the solutions of the biharmonic equation converge to the solution of Δ2u+κu=f, where κ depends on the shape of the holes and relative order of σ with respect to ε.

DOI: 10.3233/ASY-1997-153-401

Journal: Asymptotic Analysis, vol. 15, no. 3-4, pp. 203-227, 1997