A singularity perturbed nonideal transmission problem and application to the effective conductivity of a periodic composite
Résumé
We investigate the effective thermal conductivity of a two-phase composite with thermal resistance at the interface. The composite is obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material. The diameter of each inclusion is assumed to be proportional to a positive real parameter $\epsilon$ . Under suitable assumptions, we show that the effective conductivity can be continued real analytically in the parameter around the degenerate value $\epsilon= 0$, in correspondence of which the inclusions collapse to points. Part of the results presented here have been announced in [M. Dalla Riva and P. Musolino, AIP Conf. Proc. 1493, American Institute of Physics, Melville, NY, 2012, pp. 264-268].