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

In this paper we study the asymptotic behavior of the eigen-value problem solutions of the conduction process in an e-periodic domain formed by two components separated by a first-order jump interface. We prove that when e → 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.