Propagation et interaction des singularités pour les équations hyperboliques semi-linéaires en dimension 1 d'espace. (Propagation and interaction of singularities of semilinear hyperbolic equations in one space dimension) (Q915994)

The propagation and interaction of the solution singularities of the Cauchy problem \[ p(x,t,D_ x,D_ t)u(x,t)=F(x,t,u,\nabla u,...,\nabla^{m-1}u) \] are studied. These results are a continuation of those in \textit{J. Rauch} and \textit{M. Reed} [Duke Math. J. 49, 397-475 (1982; Zbl 0503.35055)] in the case of an equation of high order. They are an addition to the results of \textit{J. M. Bony} [Ann. Sci. Ec. Norm. Super., IV. Ser. 14, 209-246 (1981; Zbl 0495.35024)] for propagation of singularities of nonlinear equations as well.