Electronic Resource
Chichester, West Sussex
:
Wiley-Blackwell
Mathematical Methods in the Applied Sciences
9 (1987), S. 105-126
ISSN:
0170-4214
Keywords:
Mathematics and Statistics
;
Applied Mathematics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
Recent investigations on aperiodic waves, which are generated by time-harmonic forces in waveguides, indicate a close relationship between resonances and certain time-harmonic solutions of homogeneous boundary value problems for the wave equation (“standing waves”). This paper is motivated by the observation that, in all known cases, standing waves are connected with resonances if and only if they are subject to suitable asymptotic restrictions as |x| → ∞. These asymptotic properties are used to introduce a class of “admissible” standing waves. We prove that admissible standing waves do not exist in a certain class of local perturbations Ω of the n-dimensional domain Ω0 bounded by the hyperplanes xn = 0 and xn = π. This extends a result of M. Faulhaber on the absence of eigenvalues. As we shall show in a subsequent paper, absence of admissible standing waves implies absence of resonances.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/mma.1670090110
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