Asymptotics of eigenvalues of the Dirichlet problem in a skewed ℐ-shaped waveguide

被引：0
作者：
S. A. Nazarov
机构：
[1] St. Petersburg State University,
来源：
Computational Mathematics and Mathematical Physics | 2014年 / 54卷
关键词：
ℐ-shaped waveguide; Dirichlet problem for the Laplacian; discrete spectrum; asymptotics; boundary layer;
D O I：
暂无
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学科分类号：
摘要：
Asymptotics are constructed and justified for the eigenvalues of the Dirichlet problem for the Laplacian in a waveguide consisting of a unit strip and a semi-infinite strip joined at a small angle ɛ ∈ (0, π/2). Some properties of the discrete spectrum are established, and open questions are stated.
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页码：811 / 830
页数：19
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共 31 条
[1]  
Nazarov S A(2010)Trapped modes in a T-shaped waveguide Acoust. Phys. 56 1004-1015
[2]  
Nazarov S A(2011)Calculation of characteristics of trapped modes in T-shaped waveguides Comput. Math. Math. Phys. 51 96-110
[3]  
Shanin A V(1987)Paradoxes of limit passage in solutions of boundary value problems involving the approximation of smooth domains by polygonal domains Math. USSR Izv. 29 511-533
[4]  
Maz’ya V G(2013)The localization for eigenfunctions of the Dirichlet problem in thin polyhedra near the vertices Sib. Math. J. 54 517-532
[5]  
Nazarov S A(2003)Uniform estimates of remainders in asymptotic expansions of solutions to the problem on eigenoscillations of a piezoelectric plate J. Math. Sci. 114 1657-1725
[6]  
Nazarov S A(1953)The eigenvalues of ▿ Proc. Camb. Phil. Soc. 49 668-684
[7]  
Nazarov S A(2011) + λ Theor. Math. Phys. 167 606-627
[8]  
Jones D S(2010) = 0 when the boundary conditions are given on semi-infinite domains Sib. Math. J. 51 866-878
[9]  
Nazarov S A(2008)Asymptotic expansions of eigenvalues in the continuous spectrum of a regularly perturbed quantum waveguide Proc. London Math. Soc. 97 718-752
[10]  
Nazarov S A(2008)Variational and asymptotic methods for finding eigenvalues below the continuous spectrum threshold Russ. J. Math. Phys. 15 238-242
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