Standard

Finite-dimensional approximations to the poincaré-steklov operator for general elliptic boundary value problems in domains with cylindrical and periodic exits to infinity. / Nazarov, S. A.

In: Transactions of the Moscow Mathematical Society, Vol. 80, 01.01.2019, p. 1-51.

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

Harvard

Nazarov, SA 2019, 'Finite-dimensional approximations to the poincaré-steklov operator for general elliptic boundary value problems in domains with cylindrical and periodic exits to infinity', Transactions of the Moscow Mathematical Society, vol. 80, pp. 1-51. https://doi.org/10.1090/mosc/290

APA

Nazarov, S. A. (2019). Finite-dimensional approximations to the poincaré-steklov operator for general elliptic boundary value problems in domains with cylindrical and periodic exits to infinity. Transactions of the Moscow Mathematical Society, 80, 1-51. https://doi.org/10.1090/mosc/290

Vancouver

Nazarov SA. Finite-dimensional approximations to the poincaré-steklov operator for general elliptic boundary value problems in domains with cylindrical and periodic exits to infinity. Transactions of the Moscow Mathematical Society. 2019 Jan 1;80:1-51. https://doi.org/10.1090/mosc/290

Author

Nazarov, S. A. / Finite-dimensional approximations to the poincaré-steklov operator for general elliptic boundary value problems in domains with cylindrical and periodic exits to infinity. In: Transactions of the Moscow Mathematical Society. 2019 ; Vol. 80. pp. 1-51.

BibTeX

@article{60ee8da6c5b64574bf3f92dd652b0070,
title = "Finite-dimensional approximations to the poincar{\'e}-steklov operator for general elliptic boundary value problems in domains with cylindrical and periodic exits to infinity",
abstract = "We study formally self-adjoint boundary value problems for elliptic systems of differential equations in domains with periodic (in particular, cylindrical) exits to infinity. Statements of problems in a truncated (finite) domain which provide approximate solutions of the original problem are presented. The integro-differential conditions on the artificially formed end face are interpreted as a finite-dimensional approximation to the Steklov-Poincar{\'e} operator, which is widely used when dealing with the Helmholtz equation in cylindrical waveguides. Asymptotically sharp approximation error estimates are obtained for the solutions of the problem with the compactly supported right-hand side in an infinite domain as well as for the eigenvalues in the discrete spectrum (if any). The construction of a finite-dimensional integro-differential operator is based on natural orthogonality and normalization conditions for oscillating and exponential Floquet waves in a periodic quasicylindrical end.",
keywords = "Artificial boundary conditions, Asymptotics, Finitedimensional approximation, Floquet wave, General elliptic boundary value problem, Periodic waveguide, Poincar{\'e}-steklov operator, Truncated domain",
author = "Nazarov, {S. A.}",
year = "2019",
month = jan,
day = "1",
doi = "10.1090/mosc/290",
language = "English",
volume = "80",
pages = "1--51",
journal = "Transactions of the Moscow Mathematical Society",
issn = "0077-1554",
publisher = "American Mathematical Society",

}

RIS

TY - JOUR

T1 - Finite-dimensional approximations to the poincaré-steklov operator for general elliptic boundary value problems in domains with cylindrical and periodic exits to infinity

AU - Nazarov, S. A.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We study formally self-adjoint boundary value problems for elliptic systems of differential equations in domains with periodic (in particular, cylindrical) exits to infinity. Statements of problems in a truncated (finite) domain which provide approximate solutions of the original problem are presented. The integro-differential conditions on the artificially formed end face are interpreted as a finite-dimensional approximation to the Steklov-Poincaré operator, which is widely used when dealing with the Helmholtz equation in cylindrical waveguides. Asymptotically sharp approximation error estimates are obtained for the solutions of the problem with the compactly supported right-hand side in an infinite domain as well as for the eigenvalues in the discrete spectrum (if any). The construction of a finite-dimensional integro-differential operator is based on natural orthogonality and normalization conditions for oscillating and exponential Floquet waves in a periodic quasicylindrical end.

AB - We study formally self-adjoint boundary value problems for elliptic systems of differential equations in domains with periodic (in particular, cylindrical) exits to infinity. Statements of problems in a truncated (finite) domain which provide approximate solutions of the original problem are presented. The integro-differential conditions on the artificially formed end face are interpreted as a finite-dimensional approximation to the Steklov-Poincaré operator, which is widely used when dealing with the Helmholtz equation in cylindrical waveguides. Asymptotically sharp approximation error estimates are obtained for the solutions of the problem with the compactly supported right-hand side in an infinite domain as well as for the eigenvalues in the discrete spectrum (if any). The construction of a finite-dimensional integro-differential operator is based on natural orthogonality and normalization conditions for oscillating and exponential Floquet waves in a periodic quasicylindrical end.

KW - Artificial boundary conditions

KW - Asymptotics

KW - Finitedimensional approximation

KW - Floquet wave

KW - General elliptic boundary value problem

KW - Periodic waveguide

KW - Poincaré-steklov operator

KW - Truncated domain

UR - http://www.scopus.com/inward/record.url?scp=85083763873&partnerID=8YFLogxK

U2 - 10.1090/mosc/290

DO - 10.1090/mosc/290

M3 - Article

AN - SCOPUS:85083763873

VL - 80

SP - 1

EP - 51

JO - Transactions of the Moscow Mathematical Society

JF - Transactions of the Moscow Mathematical Society

SN - 0077-1554

ER -

ID: 60873704