Necessary conditions for hyperbolic systems

We consider the Cauchy problem for first order hyperbolic systems that have characteristic points of higher multiplicity. This means that the determinant of the principal symbol has multiple characteristic points. In the case where, on a multiple characteristic point, the principal symbol has corank 2, we give necessary conditions for the well posedness of the Cauchy problem. These conditions involve a suitably defined noncommutative determinant of the full symbol of the system. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.