Matched asymptotics approach to the construction and justification of reduced graph models for 3D Maxwell's equations in networks of thin co-axial cables
Résumé
We consider electromagnetic wave propagation in domains constituted by thin coaxial cables (made of a dielectric material which surrounds a metallic inner-wire) and a small junction. The goal is to trim down 3D Maxwell's equations in this complicated geometry to a quantum graph (see [3]) in which, along each edge, one is reduced to compute the electrical potential and current a by solving wave equations (the teleg-rapher's model) coupled by vertex conditions. In this work, using the method of matched asymp-totics, we propose improved Kirchhoff conditions and we give a rigorous justification of such a model reduction.
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