Transition from a network of thin fibers to the quantum graph : an explicitly solvable model

@inproceedings{Molchanov2006TransitionFA,
  title={Transition from a network of thin fibers to the quantum graph : an explicitly solvable model},
  author={Stanislav Molchanov and Boris Vainberg},
  year={2006}
}
We consider an explicitly solvable model (formulated in the Riemannian geometry terms) for a stationary wave process in a specific thin domain Ωε with the Dirichlet boundary conditions on ∂Ωε. The transition from the solutions of the scattering problem on Ωε to the solutions of a problem on the limiting quantum graph Γ is studied. We calculate the Lagrangian gluing conditions at vertices v ∈ Γ for the problem on the limiting graph. If the frequency of the incident wave is above the bottom of… CONTINUE READING

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