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In this paper, we study the dynamical behavior of solutions for the stochastic strongly damped wave equation with linear memory and multiplicative noise defined on Rn. Firstly, we prove the existence and uniqueness of the mild solution of certain initial value for the above-mentioned equations. Secondly, we obtain the bounded absorbing set. Lastly, We investigate the existence of a random attractor for the random dynamical system associated with the equation by using tail estimates and the decomposition technique of solutions.

Random attractors for Stochastic strongly damped non-autonomous wave equations with memory and multiplicative noise