Accession Number : AD0619957

Title :   ASYMPTOTIC EXPANSIONS OF SOLUTIONS OF INITIAL-BOUNDARY VALUE PROBLEMS FOR A DISPERSIVE HYPERBOLIC EQUATION.

Descriptive Note : Research rept.,

Corporate Author : NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES

Personal Author(s) : Bleistein,Norman ; Lewis,Robert M.

Report Date : JUN 1965

Pagination or Media Count : 43

Abstract : 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)

Descriptors :   (*BOUNDARY VALUE PROBLEMS, SERIES(MATHEMATICS)), (*SERIES(MATHEMATICS), PARTIAL DIFFERENTIAL EQUATIONS), WAVE PROPAGATION, PROPAGATION, FREQUENCY, FIELD THEORY, DIFFRACTION

Distribution Statement : APPROVED FOR PUBLIC RELEASE