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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.
в: Transactions of the Moscow Mathematical Society, Том 80, 01.01.2019, стр. 1-51.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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