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In this paper, we discuss an initial boundary value problem for thestochastic wave equation involving the nonlinear damping term $|u_t|^{q-2}u_t$and a source term of the type $|u|^{p-2}u$. We firstly establish the localexistence and uniqueness of solution by the Galerkin approximation method andshow that the solution is global for $q\geq p$. Secondly, by an appropriateenergy inequality, the local solution of the stochastic equations will blow upwith positive probability or explosive in energy sense for $p>q$.

Stochastic Wave Equations with Nonlinear Damping and Source Terms