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.

翻译：我们研究（声学）波动方程的一阶系统形式，并证明该系统的算子是从适当定义的图空间到L^2的同构映射。这一结果依赖于二阶波动方程的弱形式与超弱形式的适定性与稳定性。作为应用，我们定义并分析了一种用于求解波动方程的时空最小二乘有限元方法。文中还给出了一维和二维空间域上的数值算例。