SEMINAIRE D'ANALYSE NUMERIQUE
Année universitaire 2011-2012
Jeudi 26 avril 2012 :
Paolo MUSOLINO
(Univ. Padoue, Italie, et post-doc IRMAR)
A singularly perturbed transmission problem with non-ideal contact conditions.
We consider a perforated domain $S(\epsilon)^-$ obtained by making in $\mathbb{R}^n$ a periodic set of holes, each of them of size proportional to a positive number $\epsilon$. Then we denote by $S(\epsilon)$ the complement of $S(\epsilon)^-$. For $\epsilon$ positive and small, we consider a transmission problem with non-ideal contact conditions in the pair of domains constituted by $S(\epsilon)$ and $S(\epsilon)^-$. Problems of this kind arise in the theory of heat conduction in two-phase periodic composites with thermal resistance between the phases. We show that the solutions of such a problem can be continued real analytically in the parameter $\epsilon$ around the value $\epsilon=0$, in correspondence of which $S(\epsilon)$ and $S(\epsilon)^-$ degenerate. Our approach is based on Functional Analysis and Potential Theory and is alternative to Asymptotic Analysis.
Based on joint work with Matteo Dalla Riva, University of Aveiro.
