On the principles of limiting absorption and limit amplitude for a class of locally perturbed waveguides. Part 1: Time-independent theory
✍ Scribed by K. Morgenröther; P. Werner
- Publisher
- John Wiley and Sons
- Year
- 1988
- Tongue
- English
- Weight
- 987 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0170-4214
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✦ Synopsis
Let R be a local perturbation of the n-dimensional domain R, = R"x (0, n). In a previous papers we have introduced the notion of an admissible standing wave. We shall prove that the principle of limiting absorption holds for the Dirichlet problem of the reduced wave equation in R at o t 0 if R does not allow admissible standing waves with frequency o. From Reference 8, this condition is satisfied for every w 2 0 if l2 # R, and vex' I 0 on dR, where x' = (xlr . . . , x , -~, 0) and v is the normal unit vector on aR pointing into the complement of R. In contrast to this, the principle of limiting absorption is violated in the case of the unperturbed domain R, at the frequencies w = 1,2, . . . if n 5 3. The second part of our investigation, which will appear in a subsequent paper, is devoted to the principle of limit amplitude.