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In this paper we consider the long time behavior of solutions of the initial value problem for semi-linear wave equations of the form utt + alutlmlut Au = bluIP-lu in [0, oo) x R'. Here a, b > 0. We prove that if p > m > 1, then for any A > 0 there are choices of initial data from the energy space with initial energy E(0) = A2, such that the solution blows up in finite time. If we replace bluIP-lu by bluIP-u q(x)2u, where q(x) is a sufficiently slowly decreasing function, an analogous result holds.

Blow up of solutions of the Cauchy problem for a wave equation with nonlinear damping and source terms and positive initial energy