Homogenization of optimal control problems in variable domains. Principle of the fictitious homogenization

Article type: Research Article

Authors: Kogut, P. | Leugering, G.

Affiliations: Department of Technical Cybernetics, Dnipropetrovsk State Technical University, DIIT, Lazarjan str., 2, Dnipropetrovsk, 320010, Ukraine E‐mail: [email protected] | Fakultät für Mathematik and Physik, Universität Bayreuth, D‐95440 Bayreuth, Germany E‐mail: leugering@uni‐bayreuth.de

Abstract: We consider the optimal control problems for the linear elliptic equations in perforated domains. Each components of mathematical description of such optimal control problem depends on small parameter ε. Problems of this type appear in sensitivity analysis, perturbation theory, and homogenization of heterogenous material. We study the problem of passing to the limit within the framework of variational S‐convergence. We derive conditions under which the so‐called fictitious limiting optimal control problem can be made explicit.

Keywords: homogenization, S‐convergence, optimal control, variable domains

Journal: Asymptotic Analysis, vol. 26, no. 1, pp. 37-72, 2001