  This paper is devoted to studying the following two initial-boundary value
problems for semilinear wave equations with variable coefficients on exterior
domain with subcritical exponent in $n$ space dimensions:
u_{tt}-partial_{i}(a_{ij}(x)\partial_{j}u)=|u|^{p}, (x,t)\in
\Omega^{c}\times(0,+\infty), n\geq 3 and
u_{tt}-\partial_{i}(a_{ij}(x)\partial_{j}u)=|u_{t}|^{p}, (x,t)\in
\Omega^{c}\times (0,+\infty), n\geq 1, where $a_{ij}(x)=\delta_{ij}, when
|x|\geq R.
  The exponents $p$ satisfies $ 1<p<p_{1}(n)$ in (0.1), and $p \leq p_{2}(n)$
in (0.2), where $p_{1}(n)$ is the larger root of the quadratic equation
(n-1)p^{2}-(n+1)p-2=0, and p_{2}(n)=\frac{2}{n-1}+1, respectively. It is
well-known that the numbers p_{1}(n) and p_{2}(n) are the critical exponents.
  We will establish two blowup results for the above two initial-boundary value
problems, it is proved that there can be no global solutions no matter how
small the initial data are, and also we give the lifespan estimate of solutions
for above problems.
