HIGH-FREQUENCY ASYMPTOTICS FOR THE MODIFIED HELMHOLTZ EQUATION IN A HALF-PLANE

Base on the integral representations of the solution being derived via Fokas’ transform method, the high-frequency asymptotics for the solution of the modified Helmholtz equation, in a half-plane and subject to the Dirichlet 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.