  We are concerned with the large-time behavior of the radially symmetric
solution for multidimensional Burgers equation on the exterior of a ball
$\mathbb{B}_{r_0}(0)\subset \mathbb{R}^n$ for $n\geq 3$ and some positive
constant $r_0>0$, where the boundary data $v_-$ and the far field state $v_+$
of the initial data are prescribed and correspond to a stationary wave. It is
shown in \cite{Hashimoto-Matsumura-JDE-2019} that a sufficient condition to
guarantee the existence of such a stationary wave is $v_+<0, v_-\leq
|v_+|+\mu(n-1)/r_0$. Since the stationary wave is no longer monotonic, its
nonlinear stability is justified only recently in
\cite{Hashimoto-Matsumura-JDE-2019} for the case when $v_\pm<0, v_-\leq
v_++\mu(n-1)/r_0$. The main purpose of this paper is to verify the time
asymptotically nonlinear stability of such a stationary wave for the whole
range of $v_\pm$ satisfying $v_+<0, v_-\leq |v_+|+\mu(n-1)/r_0$. Furthermore,
we also derive the temporal convergence rate, both algebraically and
exponentially. Our stability analysis is based on a space weighted energy
method with a suitable chosen weight function, while for the temporal decay
rates, in addition to such a space weighted energy method, we also use the
space-time weighted energy method employed in
\cite{Kawashima-Matsumura-CMP-1985} and \cite{Yin-Zhao-KRM-2009}.
