Suboptimal boundary controls for elliptic equation in critically perforated domain |
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Authors: | Ciro D'Apice Umberto De Maio Peter I. Kogut |
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Affiliation: | 1. Università di Salerno, Dipartimento di Ingegneria dell''Informazione e Matematica Applicata, via Ponte don Melillo, 84084 Fisciano (SA), Italy;2. Università degli Studi di Napoli “Federico II”, Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Complesso Monte S. Angelo, via Cintia, 80126 Napoli, Italy;3. Department of Differential Equations, Dnipropetrovsk National University, Naukova str., 13, 49050 Dnipropetrovsk, Ukraine |
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Abstract: | In this paper we study the asymptotic behaviour, as ε tends to zero, of a class of boundary optimal control problems Pε, set in ε-periodically perforated domain. The holes have a critical size with respect to ε -sized mesh of periodicity. The support of controls is contained in the set of boundaries of the holes. This set is divided into two parts, on one part the controls are of Dirichlet type; on the other one the controls are of Neumann type. We show that the optimal controls of the homogenized problem can be used as suboptimal ones for the problems Pε. |
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Keywords: | 35B27 49J20 49J27 |
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