  We consider a scalar, possibly degenerate parabolic equation with a source
term, in several space dimensions. For initial data with bounded variation we
prove the existence of solutions to the initial-value problem. Then we show
that these solutions converge, in the vanishing-viscosity limit, to the
Kruzhkov entropy solution of the corresponding hyperbolic equation. The proof
exploits the H-measure compactness in several space dimensions.
