| Summary: | This work studies the homogenization of diffusion processes on
scale-free metric graphs, using weak variational formulations.
The oscillations of the diffusion coefficient along the edges of a
metric graph induce internal singularities in the global system which,
together with the high complexity of large networks constitute significant
difficulties in the direct analysis of the problem. At the same time,
these facts also suggest homogenization as a viable approach for modeling
the global behavior of the problem. To that end, we study the asymptotic
behavior of a sequence of boundary problems defined on a nested collection
of metric graphs. This paper presents the weak variational formulation of
the problems, the convergence analysis of the solutions and some
numerical experiments.
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