Finite speed of propagation for mixed problems in the $WR$ class

Abstract

In this article we are interested in the propagation speed for solutions of hyperbolic boundary value problems in the $WR$ class. Using the Holmgren principle, we show that this speed is finite and we are able to give an explicit expression for the maximal speed. Due to a propagation phenomenon along the boundary that is specific to the $WR$ class, the maximal speed can be larger than the propagation speed for the Cauchy problem. This is consistent with previous examples of the litterature.