  In this paper, we study the time-decay rate toward the planar viscous shock
wave for multi-dimensional (m-d) scalar viscous conservation law. We first
decompose the perturbation into zero and non-zero mode, and then introduce the
anti-derivative of the zero mode. Though an $L^p$ estimate and the area
inequality introduced in \cite{DHS2020}, we obtained the decay rate for planar
shock wave for n-d scalar viscous conservation law for all $n\geq1$. The
initial perturbations we studied are small, i.e.,
$\|\Phi_0\|_{H^2}\bigcap\|\Phi_0\|_{L^p}\le \varepsilon$, where $\Phi_0$ is the
anti-derivative of the zero mode of initial perturbation and $\varepsilon$ is a
small constant, see \cref{antiderivative}. It is noted that there is no
additional requirement on $\Phi_0$, i.e., $\Phi_0(x_1)$ only belongs to
$H^2(\R)$. Thus, there are essential differences from previous results, in
which the initial data is required to belong to some weighted Sobolev space,
cf.\cite{Goo1989,KM1985}. Moreover, the exponential decay rate of the non-zero
mode is also obtained.
