Well-posed Initial-boundary Value Problem for a Constrained Evolution System and Radiation-controlling Constraint-preserving Boundary Conditions

A well-posed initial-boundary value problem is formulated for the model problem of vector wave equation subject to the divergence-free constraint. Existence, uniqueness, and stability of the solution is proved by reduction to a system evolving the constraint quantity trivially, namely, the second time derivative of the constraint quantity is zero. A new set of radiationcontrolling constraint-preserving boundary conditions is constructed for the free evolution problem. Comparison between the new conditions and the standard constraint-preserving boundary conditions is made using the FourierLaplace analysis and the power series in time decomposition. The new boundary conditions satisfy the Kreiss condition and are free from the ill-posed modes growing polynomially in time.