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This paper is concerned with a class of nonlinear stochastic wave equations in Rᵈ with d 3, for which the nonlinear terms are polynomial of degree m. As an example of the nonexistence of a global solution in general, it is shown that there exists an explosive solution of some cubically nonlinear wave equation with a noise term. Then the existence and uniqueness theorems for local and global solutions in Sobolev space H₁ are proven with the degree of polynomial m 3 for d = 3, and m 2 for d = 1 or 2.
Pao–Liu Chow (Fri,) studied this question.