Time-domain decomposition of optimal control problems for the wave equation

We consider the problem of boundary optimal control of a wave equation with boundary dissipation by the way of time-domain decomposition of the corresponding optimality system. We develop an iterative algorithm which shows that the decomposed optimality system corresponds to local-in-time optimal control problems which can be treated in parallel. We show convergence of the algorithm. Finally, we provide a time discretization which is reminiscent of an instantaneous control scheme. We thereby also contribute to the problem of convergence of such schemes.