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arXiv · 2010.13318

Operator-norm resolvent asymptotic analysis of continuous media with high-contrast inclusions

Kirill D. Cherednichenko·Alexander V. Kiselev·Luis O. Silva
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Abstract

Using a generalisation of the classical notion of Dirichlet-to-Neumann map and the related formulae for the resolvents of boundary-value problems, we analyse the asymptotic behaviour of solutions to a "transmission problem" for a high-contrast inclusion in a continuous medium, for which we prove the operator-norm resolvent convergence to a limit problem of "electrostatic" type for functions that are constant on the inclusion. In particular, our results imply the convergence of the spectra of high-contrast problems to the spectrum of the limit operator, with order-sharp convergence estimates.

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BibTeXRIS

Kirill D. Cherednichenko, Alexander V. Kiselev, Luis O. Silva. 2020-10-22. Operator-norm resolvent asymptotic analysis of continuous media with high-contrast inclusions. https://doi.org/10.1134/s0001434622030051

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