On the intersection of subspaces of incoming and outgoing waves

Abstract

Many hyperbolic systems, such as the Maxwell’s and Acoustics equation,
have plane wave solutions. In the neighborhood of a boundary point,
these solutions can be conveniently decomposed in to fundamental waves
solution, which are readily classified as outgoing, incoming and
stationary or tangential.

Under broad hypothesis, we show that the spans of the outgoing and
incoming waves have nontrivial intersection. This imply that an incoming
wave may be presented as a linear combination of outgoing waves.Under
these conditions, local, linear, perfectly nonreflecting boundary
conditions are shown not to exist.

Joint work with Michael Sever