Asymptotic analysis of the scattering problem for the Helmholtz equations with high wave numbers | Zendy

Daniel Bouché | Zendy; Youngjoon Hong | Zendy; ChangYeol Jung | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Asymptotic analysis of the scattering problem for the Helmholtz equations with high wave numbers

Author(s) -

Daniel Bouché,

Youngjoon Hong,

ChangYeol Jung

Publication year - 2016

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

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research