Abstract
where u and f are m-vector-valued functions, Ai and B are m Xrm matrix-valued functions, and x = (X1, X2, . , x.n) varies over all points of the real Euclidean n-space En which have non-negative coordinates. The system (1.1) is called positive-symmetric hyperbolic if the matrices Ai are symmetric and positive-definite. Such systems are included in the general class of symmetric hyperbolic systems introduced by Friedrichs [1]. Symmetric systems are of particular interest because they possess an energy inequality; that is, the square integral of the solution over a space-like hyperplane can be estimated in terms of square integrals of initial values of the solution and the nonhomogeneous term in the differential equation. We shall not consider the Cauchy problem for (1.1), but rather, we prescribe the initial values on the coordinate hyperplanes xi= 0, i.e.,
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