In this paper, the behavior of the energy integral of the solution of a non-ideal transmission problem is investigated. Such problem appears in the study of 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, each of them of size proportional to a positive parameter $\epsilon$. Under suitable assumptions, we show that the energy integral of the solution can be continued real analytically in the parameter $\epsilon$ around the degenerate value $\epsilon=0$, in correspondence of which the inclusions collapse to points.
Energy integral of the solution of a non-ideal transmission problem in a singularly perturbed periodic domain
Musolino P.
2014
Abstract
In this paper, the behavior of the energy integral of the solution of a non-ideal transmission problem is investigated. Such problem appears in the study of 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, each of them of size proportional to a positive parameter $\epsilon$. Under suitable assumptions, we show that the energy integral of the solution can be continued real analytically in the parameter $\epsilon$ around the degenerate value $\epsilon=0$, in correspondence of which the inclusions collapse to points.Pubblicazioni consigliate
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