Problèmes de Goursat pour des systèmes semi-linéaires hyperboliques

For some semilinear hyperbolic systems of the second order with initial data on two intersecting characteristic hypersurfaces, and under a general hypothesis on the structure of the nonlinear terms, we prove that the solution of the so-called semilinear Goursat problem is defined, not only on a small neighbourhood of the intersection of these hypersurfaces, but also in a neighbourhood of the entire union of the hypersurfaces. To cite this article: D.E. Houpa, M. Dossa, C. R. Acad. Sci. Paris, Ser. I 341 (2005).