Simple waveguide junctions whose straightforward modelling leads to unsolvable boundary value problems

In this contribution the importance of the a priori evaluation of the well posedness of the models of interest is pointed out. It has been shown that even for trivial models of time-harmonic electromagnetic boundary value problems no solution can exist for infinite many regular and non pathological excitations. For these models, even the very popular technique based on the modal expansion should be considered with care since the series determining the fields in the domain do not converge. Of course, the results obtained by numerical simulators for problems involving one of the above considered dielectric configurations are completely meaningless.