Existence and finite dimensionality of the global attractor for evolution equations on unbounded domains (Q919185)

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.