The non-invariance of hyperbolicity in partial differential equations

Abstract

Hyperbolicity is shown to be not an absolute invariant in the sense defined by the author. Specifically, an example of a nonhyperbolic system is given with a partial prolongation which is hyperbolic. A large class of systems is found which is closed under modified absolute equivalence and which contains all hyperbolic systems. These ideas are applied to give existence theorems for the initial value problem in several types of nonhyperbolic systems.