Effective transmission conditions for second-order elliptic equations on networks in the limit of thin domains (Q2213059)

The authors of this article study the asymptotic behavior of solutions of uniformly elliptic partial differential equations for special domains. Precisely, those are star-shaped tubular domains with a number of non intersecting semi-infinite strips of small thickness which are connected by a central region of diameter that are proportional to the thickness of the strips. The uniform thin-domain limit is given by a partial differential equation on a network coupled with a non-linear effective transmission condition at the junction. The analysis behind this is based on ergodicity.