Well-posed initial-boundary value problem for a constrained evolution system and radiation-controlling constraint-preserving boundary conditions

Design of parallel algorithms for Einstein’s equations requires a better understanding of conditions that one can specify at the artificial boundary. The special interest is paid to conditions capable of trading “physical” radiation through the boundary. We propose a new way of constructing boundary conditions and a new way of specifying IBVPs for Einstein Equations using static constrain evolution reductions. Below we give two model problem of constrained evolution. For the first (constrained) problem, a well-posed IBVP is constructed, and a well-posed free evolution problem can be proposed based on the new approach. For the second problem, more investigation is needed to establish existence. Trivial constraint evolution reductions and stability results, however, can are obtained. 1. Vector wave equation: 3-2=1 Consider a vector wave equation in a polyhedral domain Ω