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This paper is devoted to studying the following two initial-boundary valueproblems for semilinear wave equations with variable coefficients on exteriordomain 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 andu_{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 iswell-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 valueproblems, it is proved that there can be no global solutions no matter howsmall the initial data are, and also we give the lifespan estimate of solutionsfor above problems.

Blow up of Solutions to Semilinear Wave Equations with variable coefficients and boundary