  Reaction-diffusion equations are treated on infinite networks using semigroup
methods. To blend high fidelity local analysis with coarse remote modeling,
initial data and solutions come from a uniformly closed algebra generated by
functions which are flat at infinity. The algebra is associated with a
compactification of the network which facilitates the description of spatial
asymptotics. Diffusive effects disappear at infinity, greatly simplifying the
remote dynamics. Accelerated diffusion models with conventional eigenfunctions
expansions are constructed to provide opportunities for finite dimensional
approximation.
