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

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 $\epsilon \to 0$ 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.

Keywords:

• Interfacial jump
• conduction
• eigenvalue
• two-scale convergence
• homogenization

AMS CLASSIFICATIONS:

• 35B27
• 35P15
• 49R05
• 74A50
• 80M40

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.