  Motivated by the partial differential equations of mixed type that arise in
the reduction of the Einstein equations by a helical Killing vector field, we
consider a boundary value problem for the helically-reduced wave equation with
an arbitrary source in 2+1 dimensional Minkowski spacetime. The reduced
equation is a second-order partial differential equation which is elliptic
inside a disk and hyperbolic outside the disk. We show that the reduced
equation can be cast into symmetric-positive form. Using results from the
theory of symmetric-positive differential equations, we show that this form of
the helically-reduced wave equation admits unique, strong solutions for a class
of boundary conditions which include Sommerfeld conditions at the outer
boundary.
