Ladyzhenskaya, O. A. Attractors of nonlinear evolution problems with dissipation. (Russian. English summary) Zbl 0621.35023 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 152, 72-85 (1986). The existence of a compact connected global attractor in the space \(X=W^ 2_ 2(\Omega)\times \overset\circ W^ 1_ 2(\Omega)\) for the problem \[ u_{tt}+\epsilon u_ t-\Delta u+f(u)=h(x),\quad x\in \Omega \subset {\mathbb{R}}^ 3,\quad u|_{\partial \Omega}=0, \] with cubical growth of f(u) is proved. Cited in 1 ReviewCited in 3 Documents MSC: 35G20 Nonlinear higher-order PDEs 37C70 Attractors and repellers of smooth dynamical systems and their topological structure 35B40 Asymptotic behavior of solutions to PDEs Keywords:nonlinear evolution problems; existence; compact connected global attractor; cubical growth × Cite Format Result Cite Review PDF Full Text: EuDML