Influence of non degenerated joint on the global and local behavior of joined rods

We consider transport (thermoconductivity, diffusion, etc.) problem in a system of joined n-dimensional (n = 2, 3) thin rods, We assume that the joint has the size compared with the characteristic diameter of the rods and the joint is made of materials with transport properties similar to the transport properties of materials of the rods (such joint is referred as non degenerated joint). Using a technique of local perturbation, we construct asymptotic representations of the solution and obtain the limit model for some types of rods and joints. In all the cases, we find that the non degenerated joint is ignored on the global level (e.g., in framework models) and it manifests itself on the local level (in particular, it determines the gradient of the solution in and near the joint).