Lack of independence of incoming and outgoing waves

Michael Sever

Hebrew University of Jerusalem

Abstract: We consider initial-boundary value problems for first order, symmetric hyperbolic systems of partial differential equations in unbounded spatial domains. Artificial boundary conditions, used to restrict attention to finite spatial domains, are typically formulated in terms of incoming waves at points on the artificial boundary.

Under fairly general hypotheses, we show that this strategy is nonsensical, in particular that the sets of incoming and outgoing waves at a given boundary point have finite intersection. Thus, for example, a pure incoming wave can be expressed as a sum of outgoing waves.

Under the same hypotheses, we show that local, perfectly "nonreflecting" boundary conditions, sufficient to obtain uniqueness of weak solutions, are impossible.

This is joint work with Adi Ditkowski.