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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 4, Pages 566–578 (Mi zvmmf10875)  

Asymptotic solution of the Helmholtz equation in a three-dimensional layer of variable thickness with a localized right-hand side

P. N. Petrovab, S. Yu. Dobrokhotovab

a Ishlinsky Institute for Problems of Mechanics, Russian Academy of Sciences, Moscow, Russia
b Moscow Institute of Physics and Technology, Dolgoprudny, Russia

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.

Key words: Helmholtz equation, asymptotic solutions, Maslov canonical operator, adiabatic dimension reduction.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00644_а
Russian Academy of Sciences - Federal Agency for Scientific Organizations AAAA-A17-117021310377-1
Part of the work related to analytical calculations was supported by the Russian Foundation for Basic Research (project no. 17-01-00644), and the numerical calculations were carried out within the state task no. AAAA-A17-117021310377-1.


DOI: https://doi.org/10.1134/S0044466919030074


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:4, 529–541

Bibliographic databases:

UDC: 519.632
Received: 10.07.2018

Citation: P. N. Petrov, S. Yu. Dobrokhotov, “Asymptotic solution of the Helmholtz equation in a three-dimensional layer of variable thickness with a localized right-hand side”, Zh. Vychisl. Mat. Mat. Fiz., 59:4 (2019), 566–578; Comput. Math. Math. Phys., 59:4 (2019), 529–541

Citation in format AMSBIB
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