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

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.

Original language	English
Title of host publication	Operator Theory
Subtitle of host publication	Advances and Applications
Publisher	Birkhäuser
Number of pages	62
Publication status	Acceptance date - 27 Jul 2022

Publication series

Name	Operator Theory: Advances and Applications

Keywords

math.SP
math-ph
math.AP
math.MP

Access to Document

2204.01199v1.PDFSubmitted manuscript, 833 KB

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Quantitative tools for upscaling the micro-geometry of resonant media
Cherednichenko, K.
Engineering and Physical Sciences Research Council
1/11/21 → 31/10/24
Project: Research council
Newton Mobility Grant -: Homogenisation of Degenerate Equations and Scattering for New Materials
Cherednichenko, K.
The Royal Society
1/02/17 → 31/01/19
Project: Research council
Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory
Cherednichenko, K.
Engineering and Physical Sciences Research Council
23/07/14 → 22/06/19
Project: Research council

Cite this

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title = "Asymptotic analysis of operator families and applications to resonant media",

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. ",

keywords = "math.SP, math-ph, math.AP, math.MP",

author = "Cherednichenko, {Kirill D.} and Ershova, {Yulia Yu} and Kiselev, {Alexander V.} and Ryzhov, {Vladimir A.} and Silva, {Luis O.}",

note = "62 pages, 2 figures; a survey of recent results in the area, see also arXiv:2010.13318, arXiv:1808.03961, arXiv:1703.06220, arXiv:1510.03364",

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T1 - Asymptotic analysis of operator families and applications to resonant media

AU - Cherednichenko, Kirill D.

AU - Ershova, Yulia Yu

AU - Kiselev, Alexander V.

AU - Ryzhov, Vladimir A.

AU - Silva, Luis O.

N1 - 62 pages, 2 figures; a survey of recent results in the area, see also arXiv:2010.13318, arXiv:1808.03961, arXiv:1703.06220, arXiv:1510.03364

PY - 2022/7/27

Y1 - 2022/7/27

N2 - 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.

AB - 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.

KW - math.SP

KW - math-ph

KW - math.AP

KW - math.MP

M3 - Chapter or section

T3 - Operator Theory: Advances and Applications

BT - Operator Theory

PB - Birkhäuser

ER -

Asymptotic analysis of operator families and applications to resonant media

Abstract

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Projects

Quantitative tools for upscaling the micro-geometry of resonant media

Newton Mobility Grant -: Homogenisation of Degenerate Equations and Scattering for New Materials

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

Cite this