DOMAINS OF DEPENDENCE FOR MIXED PROBLEMS FOR WAVE EQUATIONS,
NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES
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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 45395 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.