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Attractors of nonlinear evolution problems with dissipation. (Russian. English summary) Zbl 0621.35023

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.

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
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