TY - JOUR
T1 - Eigenvalues and Resonances for Domains with Tubes
T2 - Neumann Boundary Conditions
AU - Brown, Russell
AU - Hislop, P. D.
AU - Martinez, A.
PY - 1995/1/20
Y1 - 1995/1/20
N2 - We consider unbounded regions which consist of a bounded domain 𝒞 joined to an unbounded region ℰ by a tube T(ε) whose cross-section is of small diameter ε. On such a region, we consider the Laplacian with Neumann boundary conditions. We show that as ε → 0+, the spectral resonances converge to eigenvalues of 𝒞, resonances of ℰ, or eigenvalues for a two point boundary value problem on an interval of the same length as the tube. The main goal of our work is to give estimates for the rates of convergence.
AB - We consider unbounded regions which consist of a bounded domain 𝒞 joined to an unbounded region ℰ by a tube T(ε) whose cross-section is of small diameter ε. On such a region, we consider the Laplacian with Neumann boundary conditions. We show that as ε → 0+, the spectral resonances converge to eigenvalues of 𝒞, resonances of ℰ, or eigenvalues for a two point boundary value problem on an interval of the same length as the tube. The main goal of our work is to give estimates for the rates of convergence.
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U2 - 10.1006/jdeq.1995.1023
DO - 10.1006/jdeq.1995.1023
M3 - Article
AN - SCOPUS:58149363749
SN - 0022-0396
VL - 115
SP - 458
EP - 476
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2
ER -