A well-posed initial-boundary value problem is formulated for the model
problem of the 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 statically, i.e., the second time
derivative of the constraint quantity is zero. A new set of
radiation-controlling 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
Fourier-Laplace analysis and the power series decomposition in time. The new
boundary conditions satisfy the Kreiss condition and are free from the
ill-posed modes growing polynomially in time.Comment: To appear in the Journal of Hyperbolic Differential Equations. In
response to the reviewers request, a theorem on well-posedness of the free
evolution problem has been added, definitions clarified in Sections 4 and 5,
as well as a typo was removed from Section
