Linking hyperbolic and parabolic p.d.e.´s

In this article we show that from the existence and uniqueness of solutions to a hyperbolic partial differential equation (p.d.e.) existence and uniqueness of parabolic and other hyperbolic p.d.e.´s can be derived. Among others, we show that starting with the (undamped) wave equation we obtain existence and uniqueness of solutions for the uniform elliptic p.d.e.´s and for the Schrödinger equation.