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Zero resonances in local perturbations of parallel‐plane waveguides
Author(s) -
Werner P.
Publication year - 1990
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670130203
Subject(s) - mathematics , bounded function , mathematical analysis , zero (linguistics) , logarithm , scalar (mathematics) , domain (mathematical analysis) , plane (geometry) , complex plane , neumann boundary condition , boundary value problem , plane wave , geometry , physics , quantum mechanics , philosophy , linguistics
In a joint paper with K. Morgenröther [9] we have studied the propagation of scalar waves in domains of the type Ω = Ω o −B̄ with Ω o :=ℝ 2 × (0, 1), where B is a smooth bounded domain with B̄ ⊏ Ω o . In particular, we have shown that the solution of Neumann's initial and boundary value problem for the wave equation with time‐independent right‐hand side ƒ increases with a logarithmic rate as t → ∞ if the integral over ƒ does not vanish. The main purpose of the present paper is to extend this result to arbitrary smooth local perturbations of Ω o .