
Accession Number : AD0288006
Title : THE DOMAIN OF DEPENDENCE INEQUALITY AND INITIALBOUNDARY VALUE PROBLEMS FOR SYMMETRIC HYPERBOLIC SYSTEMS
Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
Personal Author(s) : WILCOX,CALVIN H.
Report Date : AUG 1962
Pagination or Media Count : 1
Abstract : The usual systems of partial differential equations that govern wave propagation (equations of acoustics, electromagnetics, magnetohydrodynamics, elasticity, etc.) have an energy integral and corresponding Poynting vector which describes the flow of energy. The most general systems of this type were introduced by K. O. Friedrichs, who called them 'symmetric hyperbolic' systems. An a priori domain of dependence inequality is proved for solutions of such systems in cylindrical spacetime domains subject to local, dissipative boundary conditions. The inequality expresses the fact that energy propagates with a finite speed in such systems. It is used to derive existence, uniqueness and regularity theorems for solutions of initialboundary value problems for symmetric hyperbolic systems. These problems provide a mathematical model for the diffraction by obstacles of the waves described by such systems. (Author)
Descriptors : *INEQUALITIES, *PARTIAL DIFFERENTIAL EQUATIONS, ENERGY, MATRICES(MATHEMATICS), WAVE PROPAGATION
Distribution Statement : APPROVED FOR PUBLIC RELEASE