Asymptotic analysis of operator families and applications to resonant media

Kirill D. Cherednichenko; Yulia Yu. Ershova; Alexander V. Kiselev; Vladimir A. Ryzhov; Luis O. Silva

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arXiv · 2204.01199

Asymptotic analysis of operator families and applications to resonant media

Kirill D. Cherednichenko·Yulia Yu. Ershova·Alexander V. Kiselev·Vladimir A. Ryzhov·Luis O. Silva

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Abstract

We give an overview of operator-theoretic tools that have recently proved useful in the analysis of boundary-value and transmission problems for second-order partial differential equations, with a view to addressing, in particular, the asymptotic behaviour of resolvents of physically motivated parameter-dependent operator families. We demonstrate the links of this rich area, on the one hand, to functional frameworks developed by S. N. Naboko and his students, and on the other hand, to concrete applications of current interest in the physics and engineering communities.

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Kirill D. Cherednichenko, Yulia Yu. Ershova, Alexander V. Kiselev, Vladimir A. Ryzhov, Luis O. Silva. 2022-04-04. Asymptotic analysis of operator families and applications to resonant media. https://arxiv.org/abs/2204.01199

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