ABOUT A CERTAIN CLASS OF PARABOLIC-HYPERBOLIC SYSTEMS OF DIFFERENTIAL EQUATIONS
We consider a class of parabolic-hyperbolic systems of differential equations that includes those of compressible viscous fluid flow. We prove the existence of solutions to the initial-boundary value problem for a short time, using analytic semigroup methods. As a byproduct we obtain that if the functions constituting the equation, but not the initial values, are infinitely differentiab1 e, then so are the solutions, expressed in Lagrange coordinates, as functions of time alone.