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Stochastic viscoelastic wave equations with nonlinear damping and source terms. (English) Zbl 1406.35174

Summary: The goal of this paper is to study an initial boundary value problem of stochastic viscoelastic wave equation with nonlinear damping and source terms. Under certain conditions on the initial data: the relaxation function, the indices of nonlinear damping, and source terms and the random force, we prove the local existence and uniqueness of solution by the Galerkin approximation method. Then, considering the relationship between the indices of nonlinear damping and nonlinear source, we give the necessary conditions of global existence and explosion in finite time in some sense of solutions, respectively.

MSC:

35L05 Wave equation
35R60 PDEs with randomness, stochastic partial differential equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
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