The graph structure impact on a singular limit of the generalized network transport

In the talk we present the family of perturbed transport problems in which a domain consists of countable intervals coupled by transition conditions at the ends. Using the theory of convergence of sequences of semigroups, we present different convergence results in the case when velocities of transport that converge to infinity are balanced by certain conditions at the boundary. We compare the structure of graph in primal problems with the properties of a network of the limit solution.
The motivation of this model is a description of proliferation of the genetic mutation. The results can be applied to give the qualitative comparison of models at the micro scale (transport equation on network) and the macro one (ODE model on the graph)