  We consider a $L^2$-contraction of large viscous shock waves for the
multi-dimensional scalar viscous conservation laws, up to a suitable shift. The
shift function depends on the time and space variables. It solves a parabolic
equation with inhomogeneous coefficients reflecting the perturbation. We
consider a suitably small $L^2$-perturbation around a viscous planar shock wave
of arbitrarily large strength. However, we do not impose any condition on the
anti-derivative variables of the perturbation around shock profile. More
precisely, it is proved that if the initial perturbation around the viscous
shock wave is suitably small in the $L^2$ norm, then the $L^2$-contraction
holds true for the viscous shock wave up to a shift function which may depend
on the temporal and spatial variables. Moreover, as the time $t$ tends to
infinity, the $L^2$-contraction holds true up to a time-dependent shift
function. In particular, if we choose some special initial perturbation, then
we can prove a $L^2$ convergence of the solutions towards the associated shock
profile up to a time-dependent shift.
