# American Institute of Mathematical Sciences

June  2019, 14(2): 411-444. doi: 10.3934/nhm.2019017

## Homogenization and exact controllability for problems with imperfect interface

 1 Dipartimento di Matematica, Università di Salerno, via Giovanni Paolo Ⅱ, 132, 84084, Fisciano (SA), Italy 2 Dipartimento di Scienze e Tecnologie, Università del Sannio, Via Port'Arsa, 11, 82100, Benevento (BN), Italy

* Corresponding author: Sara Monsurrò

Received  November 2018 Published  April 2019

The first aim of this paper is to study, by means of the periodic unfolding method, the homogenization of elliptic problems with source terms converging in a space of functions less regular than the usual $L^2$, in an $\varepsilon$-periodic two component composite with an imperfect transmission condition on the interface. Then we exploit this result to describe the asymptotic behaviour of the exact controls and the corresponding states of hyperbolic problems set in composites with the same structure and presenting the same condition on the interface. The exact controllability is developed by applying the Hilbert Uniqueness Method, introduced by J. -L. Lions, which leads us to the construction of the exact controls as solutions of suitable transposed problem.

Citation: Sara Monsurrò, Carmen Perugia. Homogenization and exact controllability for problems with imperfect interface. Networks & Heterogeneous Media, 2019, 14 (2) : 411-444. doi: 10.3934/nhm.2019017
##### References:

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##### References:
The two-component domain $\Omega$
The sets $\widehat{\Omega }^{\varepsilon }$ and $\Lambda^\varepsilon$
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