Email this article Asymptotic Solution of the Helmholtz Equation in a Three-Dimensional Layer of Variable Thickness with a Localized Right-Hand Side
- Authors: Petrov P.N.1,2, Dobrokhotov S.Y.1,2
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Affiliations:
- Ishlinsky Institute for Problems of Mechanics, Russian Academy of Sciences
- Moscow Institute of Physics and Technology
- Issue: Vol 59, No 4 (2019)
- Pages: 529-541
- Section: Article
- URL: https://journals.rcsi.science/0965-5425/article/view/180500
- DOI: https://doi.org/10.1134/S0965542519030072
- ID: 180500
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Abstract
The asymptotics of the solution to the Helmholtz equation in a three-dimensional layer of variable thickness with a localized right-hand side in the absence of “trap” states and under the asymptotic radiation conditions at infinity is constructed. The wave part of the solution has a finite number of modes. The resulting formula makes sufficiently clear the influence of the shape of the source on the wave part of the solution.
About the authors
P. N. Petrov
Ishlinsky Institute for Problems of Mechanics, Russian Academy of Sciences; Moscow Institute of Physics and Technology
Author for correspondence.
Email: petr.petrov@phystech.edu
Russian Federation, Moscow, 117526; Dolgoprudny, Moscow oblast, 141700
S. Yu. Dobrokhotov
Ishlinsky Institute for Problems of Mechanics, Russian Academy of Sciences; Moscow Institute of Physics and Technology
Author for correspondence.
Email: dobr@ipmnet.ru
Russian Federation, Moscow, 117526; Dolgoprudny, Moscow oblast, 141700
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