footnote icon A system of partial differential equations for unknowns u = (u1,...,uM )t on RN+1 of the form
0 sum N k A @0u + A @ku = b k=1

is called symmetric hyperbolic, if the matrices Ak, k = 0,...,N, are symmetric and the matrix A0 is positive definite. Both the matrices and the right hand side b may depend on the coordinates 0 1 N x ,x ,...,x and the unknowns u.