  We give a well posed initial value formulation of the
Baumgarte-Shapiro-Shibata-Nakamura form of Einstein's equations with gauge
conditions given by a Bona-Masso like slicing condition for the lapse and a
frozen shift. This is achieved by introducing extra variables and recasting the
evolution equations into a first order symmetric hyperbolic system. We also
consider the presence of artificial boundaries and derive a set of boundary
conditions that guarantee that the resulting initial-boundary value problem is
well posed, though not necessarily compatible with the constraints. In the case
of dynamical gauge conditions for the lapse and shift we obtain a class of
evolution equations which are strongly hyperbolic and so yield well posed
initial value formulations.
