Analysis reveals finitely many nonscattering wave numbers in star-shaped domains, suggesting implications for transmission eigenvalues.
.We study nonscattering phenomena associated with the time-harmonic Helmholtz equation in two dimensions. For very general classes of star-shaped domains, we show that there are at most finitely many wave numbers such that Herglotz incident waves with a fixed density function are nonscattering.
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Vogelius et al. (2025) studied this question.
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