THE INVARIANT HYPERBOLICITY CONDITIONS OF SYSTEMS AND THE REDUCTION OF SYSTEMS

The aim of this paper is to show that J. Vaillant's L conditions [43] are necessary and sufficient in order that Cauchy Problem is well pose d for a system of partial differential operators with analytic coeffic ients, when the characteristics are of constant multiplicity. Firstly, we recall L conditions for systems, in the general case, and we reduc e it, using a theorem of W. Matsumoto, to a normal form, where we can read hyperbolicity. Then, we give the calculations needed to show inva riance under conjugation byoperators of change of order (that are used in the proof of W. Matsumoto's theorem), when the multiplicity is fiv e.