{\cal S} = \{t = 0, |x| \le R\},$$ and boundary conditions $$\label{boundary-cond}
B^{\mu}\,\phi_{,\,\mu} = h  \quad \mbox{on} \quad   {\cal T} = \{t \ge 0, |x| = R\},$$ which are defined in terms of the vector field $$\label{M-def}
B = (1 + e)\,T_* + (1 - e)\,N,$$ on ${\cal T}$, where $T_*$ denotes the future directed time-like unit vector field $\partial_t$ tangential to ${\cal T}$, $N$ the outward directed unit normal to ${\cal T}$, and $$\label{e-def}
e \in C^{\infty}({\cal T}, \mathbb{R}), \quad \quad |e| \le 1,$$ is a given function. The initial data $\phi_0$, $\phi_1$, the boundary data $h$, and $f$ are given real-valued functions which are assumed to be smooth.

The authors of [@kreiss:et:al:2009] consider more general boundary conditions. They require $|e| < 1$ in (\[boundary-cond\]) but admit arbitrary future directed, unit time-like vector fields $T$ tangential to ${\cal T}$ instead of $T_*$ and allow for right hand sides of much more general form. The problem posed above suffices to illustrate the points we wish to discuss.

Clearly, it can only have a solution which is smooth if the data satisfy certain [*consistency conditions*]{} along the edge $$\Sigma = \{t = 0, |x| = R\} = {\cal S} \cap 