The Interior Transmission Problem in Acoustics and Electromagnetics

Peter Monk
University of Delaware

As a result of studies of the far field pattern of the

scattered wave for time harmonic acoustic and electromagnetics, a

new class of interior problem arises termed the "Interior

Transmission Problem" (ITP). The ITP is not a standard elliptic

problem, and a study of the solvability of this problem gives rise

to a non-standard eigenvalue problem for the ITP. The proof of

existence and properties of these eigenvalues is not

straightforward. I shall survey the ITP and its properties in

several applications, and describe numerical schemes for computing

transmission eigenvalues. Remarkably, transmission eigenvalues can

be observed from far field data, and the resulting eigenvalues can

be used to estimate properties of the scatterer. The interior

transmission problem has similarities with problems involving

negative index of refraction, so it may be that the study of

interior transmission eigenvalues is also relevant there.

Presentation (PDF File)

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