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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 13
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Articles

Two-temperature homogenized eigenfunctions of conduction through domains with jump interfaces

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Pages 2361-2370 | Received 18 Sep 2018, Accepted 20 Dec 2018, Published online: 11 Jan 2019
 

ABSTRACT

In this paper we study the asymptotic behavior of the eigenvalue problem solutions of the conduction process in an ϵ-periodic domain formed by two components separated by a first-order jump interface. We prove that when ε0 the limits of the eigenvalues and eigenfunctions of this problem verify a certain (effective) two-temperature eigenvalue problem. Moreover, we show that the effective eigenvalue problem has only eigenvalues which come from the homogenization process.

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Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors gratefully acknowledge partial support by the International Network GDRI ECO-Math.

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