Mathematical analysis reveals transmission eigenvalue-free regions near the real axis under strong damping, indicating behavioral parallels to weakly damped systems.
We consider interior transmission problems with one complex-valued refraction index independent of the spectral parameter, that is, with a strong damping term, and we suppose that it does not vanish on the boundary. Under some quite general conditions, we obtain transmission eigenvalue-free regions similar to those obtained by the author in the case of weak damping.
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Georgi Vodev (2026) studied this question.
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