Characteristic decomposition of the quasilinear strictly hyperbolic systems

This paper is devoted to extending the well-known result on reducible equations in Courant and Friedrichs’ book “Supersonic flow and shock waves”, that any hyperbolic state adjacent to a constant state must be a simple wave. We establish a nice sufficient condition for the existence of characteristic decompositions to the general 2 × 2 quasilinear strictly hyperbolic systems. These decompositions allow for a proof that any wave adjacent to a constant state is a simple wave, despite the fact that the coefficients depend on the independent variables. Consequently as applications, we obtain the same results for the pseudo-steady Euler equations.