Difficulties in Recognizing Ill-Posed Electromagnetic Problems Involving Wrong Effective Models of Media

The set of ill-posed time-harmonic electromagnetic boundary value problems is shown to be much richer than expected so far, when all fine details of composite media are neglected and effective media, possibly anisotropic, are considered. This result seems to suggest that it can be extremely difficult to identify wrong formulations of electromagnetic boundary value problems also because, unfortunately, numerical simulations with common discretizations could give no help in recognizing them.