INTERACTION OF PRINCIPAL SYMBOLS FOR SEMILINEAR MONODIMENTIONAL CONORMAL WAVES

We consider the semi-linear problem for a first order strictly hyperbo lic system with any size greater than or equal to 3, and one space var iable. We study the interaction of two conormal singularities carried by two characteristics Sigma(1), Sigma(2), and we give precisely the p rincipal symbol's expression of the solution on all the forward charac teristics from the point of intersection. On the forward characteristi cs, except Sigma(1) and Sigma(2), roe get a sum law, which generalizes the one given by J. Rauch and M. Reed [3] in the case of piecewise sm ooth functions, and which improves the J.-M. Bony [1] and Wang Weike [ 6] results in the one space variable case.