A Singularly Perturbed Nonideal Transmission Problem and Application to the Effective Conductivity of a Periodic Composite

Autores: Matteo dalla Riva, Paolo Musolino
Localización: Siam journal on applied mathematics, ISSN 0036-1399, Vol. 73, Nº 1, 2013, págs. 24-46
Idioma: inglés
DOI: 10.1137/120886637
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Resumen
- 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 $\epsilon$ 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].