The aim of this paper is to provide the correctors associated to the homogenization of a parabolic problem describing the heat
transfer. The results here complete the earlier study in [Jose, Rev. Roumaine Math. Pures Appl.
54 (2009) 189–222]
on the asymptotic behaviour of a problem in a domain with two components separated by an ε-periodic interface.
The physical model established in [Carslaw and Jaeger, The Clarendon Press, Oxford (1947)] prescribes on the interface the
condition that the flux of the temperature is proportional to the jump of the temperature field, by a factor of order
We suppose that -1 < γ ≤ 1. As far as the energies of the homogenized problems are concerned, we consider the cases
-1 < γ < 1
and γ = 1 separately. To obtain the convergence of the energies, it is necessary to impose stronger assumptions on the data.
in [Jose, Rev. Roumaine Math. Pures Appl.
54 (2009) 189–222] and [Faella and Monsurrò, Topics on Mathematics for
Smart Systems, World Sci. Publ., Hackensack, USA (2007) 107–121] (also in [Donato et al., J. Math. Pures Appl.
87 (2007) 119–143]), the case γ = 1 is more interesting because of the presence of a memory effect
in the homogenized problem.