List of Footnotes

1 It might be worthwhile to point out that the notion of regularity of the system of equations has nothing whatsoever to do with the regularity of its solutions. While the former is a formal property of the system which can be established simply by inspection, the latter is usually rather difficult to establish because it involves detailed investigations of the appropriate well-posed problems.
2 A system of partial differential equations for unknowns u = (u1,...,uM )t on ℝN+1 of the form
∑N A0∂0u + Ak ∂ku = b k=1
is called symmetric hyperbolic, if the matrices k A, k = 0,...,N, are symmetric and the matrix 0 A 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.