  Callan, Giddings, Harvey and Strominger (CGHS) previously introduced a
two-dimensional semiclassical model of gravity coupled to a dilaton and to
matter fields. Their model yields a system of field equations which may
describe the formation of a black hole in gravitational collapse as well as its
subsequent evaporation. Here we present an approximate analytical solution to
the semiclassical CGHS field equations. This solution is constructed using the
recently-introduced formalism of flux-conserving hyperbolic systems. We also
explore the asymptotic behavior at the horizon of the evaporating black hole.
