High-Frequency Asymptotics for the Helmholtz Equation in a Half-Plane
Huang Min-hai · Journal of Nonlinear Mathematical Physics · 2012
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.