  We consider the initial-boundary value problem of semilinear wave equation
with nonlinearity $|u|^p$ in exterior domain in $\mathbf{R}^N$ $(N\geq 3)$.
Especially, the lifespan of blowup solutions with small initial data are
studied. The result gives upper bounds of lifespan which is essentially the
same as the Cauchy problem in $\mathbf{R}^N$. At least in the case $N=4$, their
estimates are sharp in view of the work by Zha--Zhou (2015). The idea of the
proof is to use special solutions to linear wave equation with Dirichlet
boundary condition which are constructed via an argument based on
Wakasa--Yordanov.
