Open AccessAsymptotic analysis of the scattering problem for the Helmholtz equations with high wave numbers
Author(s) -
Daniel Bouché,
Youngjoon Hong,
Chang-Yeol Jung
Publication year - 2017
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2017048
Subject(s) - helmholtz equation , bessel function , mathematical analysis , scattering , limit (mathematics) , boundary value problem , asymptotic analysis , mathematics , dirichlet boundary condition , method of matched asymptotic expansions , asymptotic expansion , wkb approximation , physics , boundary (topology) , wave equation , optics , quantum mechanics
We study the asymptotic behavior of the two dimensional Helmholtz scattering problem with high wave numbers in an exterior domain, the exterior of a circle. We impose the Dirichlet boundary condition on the obstacle, which corresponds to an incidental wave. For the outer boundary, we consider the Sommerfeld conditions. Using a polar coordinates expansion, the problem is reduced to a sequence of Bessel equations. Investigating the Bessel equations mode by mode, we find that the solution of the scattering problem converges to its limit solution at a specific rate depending on k.clos