Asymptotic Expansions of Solutions of Initial-Boundary Value Problems for a Dispersive Hyperbolic Equation

摘要

Initial-boundary value problems for an energy conserving dispersive hyperbolic equation, the Klein-Gordon equation, are considered. This equation exhibits the main feature of dispersion: The speed of propagation depends on frequency. Problems in two space dimensions with a parabolic boundary are discussed. The primary purpose of this paper is to compare the asymptotic expansion of solutions obtained by a technique we call the ray method with the asymptotic expansion of the exact solution. In the cases considered, the solutions agree. In addition a numerical comparison is made of the exact and asymptotic solutions for a specified region of space time. (Author)