Diffusion Processes and PDE’s in Narrow Branching Tubes

Abstract

Consider a connected graph Γ in R^r with vertices O₁,…, O _m and edges I₁,…, I _n . Let G^∈ be a domain consisting of narrow tubes surrounding the edges I _i ⊂ Γ and of small neighborhoods ε _k of the vertices O _k ⊂ Γ (see Fig. 16).