On the intersection of sets of incoming and outgoing waves

Abstract

In the neighborhood of a boundary point, the solution of a first-order symmetric homogenous hyperbolic system is conveniently decomposed into fundamental waves solutions that are readily classified as outgoing, incoming, and stationary, or tangential. Under a broad hypothesis, we show that the spans of the sets of outgoing and incoming waves have nontrivial intersection. Under these conditions, local, linear, perfectly nonreflecting local boundary conditions are shown to be an impossibility.