A singularly perturbed nonideal transmission problem and application to the effective conductivity of a periodic composite

Matteo Dalla Riva*, Paolo Musolino

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (SciVal)

Abstract

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 ε. Under suitable assumptions, we show that the effective conductivity can be continued real analytically in the parameter ε around the degenerate value ε = 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].

Original languageEnglish
Pages (from-to)24-46
Number of pages23
JournalSIAM Journal on Applied Mathematics
Volume73
Issue number1
DOIs
Publication statusPublished - 02 Jan 2013

Keywords

  • Effective conductivity
  • Nonideal contact conditions
  • Periodic composite
  • Real analytic continuation
  • Singularly perturbed domain
  • Transmission problem

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