Journal Article

Gap phenomenon in the homogenization of parabolic optimal control problems

C. D'Apice, U. De Maio and P. I. Kogut

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 25, issue 4, pages 461-489
Published in print December 2008 | ISSN: 0265-0754
Published online October 2008 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dnn010
Gap phenomenon in the homogenization of parabolic optimal control problems

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In this paper, we study the asymptotic behaviour of a parabolic optimal control problem in a domain Ωϵ ⊂ , whose boundary ∂Ωϵ contains a highly oscillating part. We consider this problem with two different classes of Dirichlet boundary controls, and, as a result, we provide its asymptotic analysis with respect to the different topologies of homogenization. It is shown that the mathematical descriptions of the homogenized optimal control problems have different forms and these differences appear not only in the state equation and boundary conditions but also in the control constraints and the limit cost functional.

Keywords: optimal control problem; homogenization; thick multi-structure; variational convergence; set convergence; gap phenomenon

Journal Article.  0 words. 

Subjects: Mathematics

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