### Global solutions and exponential decay for a nonlinear coupled system of beam equations of Kirchhoff type with memory in a domain with moving boundary.

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We report on new results concerning the global well-posedness, dissipativity and attractors for the quintic wave equations in bounded domains of ${\mathbb{R}}^{3}$ with damping terms of the form ${(-{\Delta}_{x})}^{\theta}{\partial}_{t}u$, where $\theta =0$ or $\theta =1/2$. The main ingredient of the work is the hidden extra regularity of solutions that does not follow from energy estimates. Due to the extra regularity of solutions existence of a smooth attractor then follows from the smoothing property when $\theta =1/2$. For $\theta =0$ existence of smooth attractors is more complicated and follows...