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The dynamical behavior of a stochastic wave equation on a bounded domain in R3 with smooth boundary, for which the nonlinear damping has a critical cubic growth rate, is investigated. Its dissipativeness in higher-energy spaces Ws,2×Ws−1,2 for 1<s⩽2 is established. This implies that the random dynamical system (RDS) generated by the equation has a random attractor in H01×L2, which is a tempered...
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