Global non-existence for some nonlinear wave equations with damping and source terms in an inhomogeneous medium.

In this paper we study the initial value problem for the nonlinear wave equation with damping and source terms with some $\rho(x)$ and $f(u)$ on the whole space $\mathbb{R}^{n}$ ( $n\geq 3$ ). For the low initial energy case, which is the non-positive initial energy, based on a concavity argument we prove the blow-up result. As for the high initial energy case, we give sufficient conditions of the initial data such that the corresponding solution blows up in finite time. In other words, our results imply a complete blow-up theorem in the sense of the initial energy, $-\infty< E(0)<+\infty$ . [ABSTRACT FROM AUTHOR]