A GENERAL APPROACH TO THE NONLINEAR HYPERBOLIC CAUCHY PROBLEM WITH CONSTANT MULTIPLICITY

We describe a way to solve locally the Cauchy problem for nonlinear hyperbolic equations with characteristic roots of constant multiplicity. A universal reduction to a first order system gives the optimal space of well posedness under different assumptions on the lower order terms or on the regularity of the equation. The method gives also the propagation of the analytic regularity of the solution in domains of influence.