  We study a scalar integro-differential conservation law. The equation was
first derived in [2] as the slow erosion limit of granular flow. Considering a
set of more general erosion functions, we study the initial boundary value
problem for which one can not adapt the standard theory of conservation laws.
We construct approximate solutions with a fractional step method, by
recomputing the integral term at each time step. A-priori L^\infty bounds and
BV estimates yield convergence and global existence of BV solutions.
Furthermore, we present a well-posedness analysis, showing that the solutions
are stable in L^1 with respect to the initial data.
