Functional model for boundary-value problems

Kirill d. Cherednichenko; Alexander v. Kiselev; Luis o. Silva

doi:10.1112/mtk.12092

Functional model for boundary-value problems

Kirill d. Cherednichenko, Alexander v. Kiselev, Luis o. Silva

University of Bath
Departamento de Física Matemática Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas Universidad Nacional Autónoma de México C.P. 04510 México D.F.
International Research Laboratory “Multiscale Model Reduction” Ammosov North‐Eastern Federal University Yakutsk Russia
Saint Petersburg State University 7/9 University Embankment St. Petersburg 199034 Russia

Research output: Contribution to journal › Article › peer-review

4 Citations (SciVal)

Abstract

We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric operators in terms of appropriate Dirichlet-to-Neumann maps, which can be utilised in the analysis of the properties of parameter-dependent problems, including the study of their spectra.

Original language	English
Pages (from-to)	596 - 626
Number of pages	31
Journal	Mathematika
Volume	67
Issue number	3
Early online date	7 May 2021
DOIs	https://doi.org/10.1112/mtk.12092
Publication status	Published - 31 Jul 2021

Bibliographical note

Funding Information:
We are grateful to the referee for providing helpful?comments.

Publisher Copyright:
© 2021 The Authors. Mathematika is copyright © University College London.

Keywords

47A45 (primary)
47F05

ASJC Scopus subject areas

General Mathematics

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10.1112/mtk.12092Licence: CC BY

https://onlinelibrary.wiley.com/doi/10.1112/mtk.12092

Cite this

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title = "Functional model for boundary-value problems",

abstract = "We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric operators in terms of appropriate Dirichlet-to-Neumann maps, which can be utilised in the analysis of the properties of parameter-dependent problems, including the study of their spectra.",

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author = "Cherednichenko, {Kirill d.} and Kiselev, {Alexander v.} and Silva, {Luis o.}",

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AU - Kiselev, Alexander v.

AU - Silva, Luis o.

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N2 - We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric operators in terms of appropriate Dirichlet-to-Neumann maps, which can be utilised in the analysis of the properties of parameter-dependent problems, including the study of their spectra.

AB - We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric operators in terms of appropriate Dirichlet-to-Neumann maps, which can be utilised in the analysis of the properties of parameter-dependent problems, including the study of their spectra.

KW - 47A45 (primary)

KW - 47F05

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U2 - 10.1112/mtk.12092

DO - 10.1112/mtk.12092

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JO - Mathematika

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Functional model for boundary-value problems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

Cite this

Functional model for boundary-value problems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

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

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

Cite this