Homogenization of a semilinear elliptic problem in a thin composite domain with an imperfect interface

In this paper, we consider the asymptotic behavior of a semilinear elliptic problem in a thin two-composite domain with an imperfect interface, where the flux is discontinuous. For this thin domain, both the height and the period are of order epsilon. We first use Minty-Browder theorem to prove the well-posedness of the problem and then apply the periodic unfolding method to obtain the limit problems and some corrector results for three cases of a real parameter gamma = -1, gamma is an element of (-1, 1) and gamma < -1, respectively. To deal with the semilinear terms, the extension operator and the averaged function are used.