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

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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

Author(s):
Bleistein, Norman ; Lewis, Robert M.
Author Organization(s):
NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES
Descriptive Note:
Research rept.,
Annotation:
Asymptotic expansions of solutions of initial-boundary value problems for a dispersive hyperbolic equation.
Pagination:
0043

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release

RECORD

Collection: TR
Identifying Numbers
Report Number(s):
RR-EMp-207, AFCRL-65-456
Contract/Grant Number(s):
AF19 628 4065
Task Number(s):
460302
Project Number(s):
4603
Monitor Series:
65-456
 Subject Terms
Communities of Interest:
No COI(s) Identified
Descriptor(s):
(*BOUNDARY VALUE PROBLEMS, SERIES(MATHEMATICS)), (*SERIES(MATHEMATICS), PARTIAL DIFFERENTIAL EQUATIONS), WAVE PROPAGATION, PROPAGATION, FREQUENCY, FIELD THEORY, DIFFRACTION
Keyword(s):
KLEIN GORDON EQUATION
Report Date:
1965 Jun 01