Optimal control for a hyperbolic problem in composites with imperfect interface: A memory effect

Luisa Faella; Carmen Perugia

doi:10.3934/eect.2017011

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2017, Volume 6, Issue 2: 187-217. Doi: 10.3934/eect.2017011

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Optimal control for a hyperbolic problem in composites with imperfect interface: A memory effect

Luisa Faella^1, and
Carmen Perugia^2, ,

1.
Dipartimento di Ingegneria Elettrica e dell' Informazione, Università degli Studi di Cassino e del Lazio Meridionale, via G. Di Biasio 43, Cassino, 03043, Italia
2.
Dipartimento di Scienze e Tecnologie, Università del Sannio, Via Port' Arsa 11, Benevento, 82100, Italia

* Corresponding author: Carmen Perugia
* Corresponding author: Carmen Perugia

Received: August 31, 2016

Revised: December 31, 2016

Published: May 2017

Author's contributions: The authors conceived and wrote this article in collaboration and with same responsibility. All of them read and approved the final manuscript

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Abstract

We study an optimal control problem for certain evolution equations in two component composites with $\varepsilon$-periodic disconnected inclusions of size $\varepsilon$ in presence of a jump of the solution on the interface that varies according to a parameter $γ$. In particular the case $γ=1$ is examinated.

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Mathematics Subject Classification: 35B27, 35L10, 49J20, 93C20.

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Figure 1. $\Omega_{\varepsilon}$

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