Random dynamics of a coupled structurally damped wave system

This paper is concerned with the long-time behavior of a coupled system of structurally damped wave equations posed on a bounded domain in $ \mathbb{R}^3 $, in which the coupling coefficient is random and driven by a metric dynamical system. Under appropriate dissipativity and growth conditions on the nonlinearity, we first establish the well-posedness of the problem and construct an associated continuous random dynamical system. We then prove the existence of a unique random attractor by means of a tempered absorbing set and a random stabilizability estimate that ensures pullback asymptotic compactness. In addition, we show that this random attractor has finite fractal dimension.