Two-scale convergence of periodic elliptic spectral problems with indefinite density function in perforated domains

Article type: Research Article

Authors: Douanla, Hermann

Affiliations: Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg, SE-41296, Sweden. E-mail: douanla@chalmers.se

Abstract: Spectral asymptotics of linear periodic elliptic operators with indefinite (sign-changing) density function is investigated in perforated domains with the two-scale convergence method. The limiting behavior of positive and negative eigencouples depends crucially on whether the average of the weight over the solid part is positive, negative or equal to zero. We prove concise homogenization results in all three cases.

Keywords: homogenization, eigenvalue problems, perforated domains, indefinite weight function, two-scale convergence

DOI: 10.3233/ASY-2012-1127

Journal: Asymptotic Analysis, vol. 81, no. 3-4, pp. 251-272, 2013