Homogenization and correctors for the hyperbolic problems with imperfect interfaces via the periodic unfolding method

Abstract

In this paper, we study the homogenization and corrector results forthe hyperbolic problem in a two-component composite with$\varepsilon$-periodic connected inclusions. The condition prescribed onthe interface is that a jump of the solution is proportional to theconormal derivatives via a function of order $\varepsilon^\gamma$($\gamma < -1$). The main ingredient of the proof of our main theoremsis the time-dependent periodic unfolding method in two-componentdomains. Our homogenization results recover those of the corresponding case in [Donato, Faella and Monsurrò, J.Math. Pures Appl. 87 (2007), pp. 119-143]. We also derive thecorresponding corrector results.