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Existence and finite dimensionality of the global attractor for evolution equations on unbounded domains. (English) Zbl 0706.35058

The asymptotic behaviour of solutions of nonlinear parabolic equations on unbounded domains is studied. In order to compensate the lack of compactness in the Sobolev imbedding, a time-dependent weight is introduced, which becomes effective for large times. The existence of a global attractor is then proved for several examples, and the finite fractal dimensionality of this attractor is established.
Reviewer: F.Abergel

MSC:

35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
34D45 Attractors of solutions to ordinary differential equations
35B40 Asymptotic behavior of solutions to PDEs
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