On the mixed problem for non strictly hyperbolic operators

The classical theory of strictly hyperbolic boundary value problems has received several extensions since the 70’s. One of the most noticeable is the result of Metivier establishing that Majda’s "block structure condition" for constantly hyperbolic operators, which implies well-posedness for the initial boundary value problem (IBVP) with zero initial data. The well-posedness of IBVP with non zero initial requires that “L be a continuable initial data”. For strictly hyperbolic systems, this result was proven by Rauch. We prove here by using classical matrix theory that his fundamental a priori estimates are valid for constantly hyperbolic IBVP.