  This note studies a four-field hyperbolic PDE model that was recently
introduced by Bemfica, Disconzi, and Noronha for the pure radiation fluid with
viscosity, and asks whether shock waves admit continuous profiles in this
description. The model containing two free parameters mu, nu and being causal
whenever one chooses (mu,nu) from a certain range C subset R2, this paper shows
that for any choice of (mu,nu) in the interior of C, there is a dichotomy in so
far as (i) shocks of sufficiently small amplitude admit profiles and (ii)
certain other, thus necessarily non-small, shocks do not. This finding does not
preclude the possibility that if one chooses (mu,nu) from a specific part S of
the boundary of C, the dichotomy disappears and all shocks have profiles; the
parameter set S corresponds to the "sharply causal" case, in which one of the
characteristic speeds of the dissipation operator is the speed of light.
