
Accession Number : AD0618990
Title : DOMAINS OF DEPENDENCE FOR MIXED PROBLEMS FOR WAVE EQUATIONS,
Corporate Author : NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES
Personal Author(s) : Zauderer,Erich
Report Date : 12 AUG 1963
Pagination or Media Count : 10
Abstract : The energy integral method in its usual form involving the use of the characteristic conoid is easily extended to yield a uniqueness theorem for mixed problems for the wave equation. Friedlander ('Sound pulses.' Cambridge, Cambridge Univ. Press, 1958. Proc. of the Cambridge Philosophical Society 45:395 (1949)) noted this and used it to determine the fronts of disturbances in the shadow region resulting from mixed problems with homogeneous boundary conditions. It is shown how these fronts may be used to obtain a uniqueness theorem for such mixed problems with smooth boundaries, and, thereby, domains of dependence and influence for such problems, with homogeneous boundary conditions. These domains are smaller than those obtained from the usual energy integral method referred to above and coincide with those of the solutions of several particular mixed problems.
Descriptors : (*PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS), (*SET THEORY, PARTIAL DIFFERENTIAL EQUATIONS), INTEGRALS, GEOMETRY, FUNCTIONAL ANALYSIS
Distribution Statement : APPROVED FOR PUBLIC RELEASE