  In this paper, we discuss the asymptotic behaviour of weak solutions to the
Cauchy problem toward the viscous shock waves for the scalar viscous
conservation law. We firstly consider the case that the flux function is the
quadratic Burgers flux and obtain the time-decay rate in $L^\infty$-norm for
the cases with degenerate $p$-Laplacian viscosity and with linear viscosity,
respectively. Moreover, we also give the time-decay rate in $L^\infty$-norm
with general flux and linear viscosity. All of these results do not involve
smallness conditions on the initial data.
