On the attractors of nonlinear evolution problems

She existence of a compact connected global attractor in the space $X=W_2^2(\Omega)\times W_2^1(\Omega)$ for the problem $u_{tt}+\varepsilon u_t-\Delta u+f(u)=h(x)$, $x\in\Omega\subset\mathbb R^3$, $u|_{\partial\Omega}=0$, with cubical growth of $f(u)$ is prooved.