The aim of this work will be to consider the continuity of the asymptotic dynamics for semilinear parabolic and hyperbolic problems under singular perturbations. We will be particularly interested in the cases when the spatial domínio is unbounded. The existence and upper semicontinuity of global attractors for this problems have been considered before whereas the lower semicontinuity has been sistematically neglected. Our aim is to seek ways to consider the lower semicontinuity. Questions related to the non-autônomos case will also be treated.
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