The Non-Invariance of Hyperbolicity in Partial Differential Equations

摘要

Hyperbolicity is shown to be not an absolute invariant in the sense defined in. Specifically, an example of a non-hyperbolic 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 non-hyperbolic systems. (Author)