  We focus on the initial boundary value problem for a general scalar balance
law in one space dimension. Under rather general assumptions on the flux and
source functions, we prove the well-posedness of this problem and the stability
of its solutions with respect to variations in the flux and in the source
terms. For both results, the initial and boundary data are required to be
bounded functions with bounded total variation. The existence of solutions is
obtained from the convergence of a Lax-Friedrichs type algorithm with operator
splitting. The stability result follows from an application of Kru\v{z}kov's
doubling of variables technique, together with a careful treatment of the
boundary terms.
