  We study a first-order system formulation of the (acoustic) wave equation and
prove that the operator of this system is an isomorphsim from an appropriately
defined graph space to L^2. The results rely on well-posedness and stability of
the weak and ultraweak formulation of the second-order wave equation. As an
application we define and analyze a space-time least-squares finite element
method for solving the wave equation. Some numerical examples for one- and two-
dimensional spatial domains are presented.
