Volume 19, Issue 1, March 2012, Pages 38 - 47
High-Frequency Asymptotics for the Helmholtz Equation in a Half-Plane
Authors
Min-Hai Huang
College of Mathematics and Information Sciences, Zhaoqing University, Zhaoqing, GuangDong 526061, P. R. China
Department of Mathematics, ZhongShan University, GuangZhou 510275, P. R. China,hmh9520@sina.com
Received 18 April 2011, Accepted 28 September 2011, Available Online 6 January 2021.
- DOI
- 10.1142/S1402925112500040How to use a DOI?
- Keywords
- High-frequency asymptotics; Fokas' transform method; method of steepest descents; Helmholtz equation; Neumann condition
- Abstract
Base on the integral representations of the solution being derived via Fokas' transform method, the high-frequency asymptotics for the solution of the Helmholtz equation, in a half-plane and subject to the Neumann condition is discussed. For the case of piecewise constant boundary data, full asymptotic expansions of the solution are obtained by using Watson's lemma and the method of steepest descents for definite integrals.
- Copyright
- © 2012 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Min-Hai Huang PY - 2021 DA - 2021/01/06 TI - High-Frequency Asymptotics for the Helmholtz Equation in a Half-Plane JO - Journal of Nonlinear Mathematical Physics SP - 38 EP - 47 VL - 19 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925112500040 DO - 10.1142/S1402925112500040 ID - Huang2021 ER -