  A class of semi-linear hyperbolic systems in 1+1 dimensions was investigated
several years ago by Ori and Gorbonos. This class, to which we shall refer as
"flux-conserving systems", exhibits a variety of interesting mathematical
properties. Here we demonstrate how the formalism of flux-conserving systems
can be applied to the problem of black-hole evaporation in 1+1-dimensions. More
specifically, we show how the semiclassical CGHS field equations may be
approximated by a certain flux-conserving system.
